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How can a graph, table, ordered pair, or an algebraic rule help describe the relationship between two variables?

How can we track the change in a quantity over time and how is this useful when making decisions?

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In the 1980s and 1990s, the Cultural Orientation Resource Center was funded to develop phrasebooks for selected refugee populations. These phrasebooks include appropriate English phrases for use in daily American life, selected to be direct, brief, and relevant. Among the nineteen units included are sections on Giving Information About Yourself, Recognizing Signs, Dealing With Money, Health, Food, Clothing, Housing, and Jobs.

The COR Center is not currently developing such phrasebooks in the languages of newly-arriving refugee populations, yet these publications may still be useful to some refugees and their service providers.

Each phrasebook is approximately 140 pages and can be downloaded for free.

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In the 1980s and 1990s, the Cultural Orientation Resource Center was funded to develop phrasebooks for selected refugee populations. These phrasebooks include appropriate English phrases for use in daily American life, selected to be direct, brief, and relevant. Among the nineteen units included are sections on Giving Information About Yourself, Recognizing Signs, Dealing With Money, Health, Food, Clothing, Housing, and Jobs.

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Auditory

If you are an auditory learner, you learn by hearing and listening. You understand and remember things you have heard. You store information by the way it sounds, and you have an easier time understanding spoken instructions than written ones. You often learn by reading out loud because you have to hear it or speak it in order to know it.

As an auditory learner, you probably hum or talk to yourself or others if you become bored. People may think you are not paying attention, even though you may be hearing and understanding everything being said.

Here are some things that auditory learners like you can do to learn better.

Sit where you can hear.

Have your hearing checked on a regular basis.

Use flashcards to learn new words; read them out loud.

Read stories, assignments, or directions out loud.

Record yourself spelling words and then listen to the recording.

Have test questions read to you out loud.

Study new material by reading it out loud.

Remember that you need to hear things, not just see things, in order to learn well.

Visual

If you are a visual learner, you learn by reading or seeing pictures. You understand and remember things by sight. You can picture what you are learning in your head, and you learn best by using methods that are primarily visual. You like to see what you are learning.

As a visual learner, you are usually neat and clean. You often close your eyes to visualize or remember something, and you will find something to watch if you become bored. You may have difficulty with spoken directions and may be easily distracted by sounds. You are attracted to color and to spoken language (like stories) that is rich in imagery.

Here are some things that visual learners like you can do to learn better:

Sit near the front of the classroom. (It won't mean you're the teacher's pet!)

Have your eyesight checked on a regular basis.

Use flashcards to learn new words.

Try to visualize things that you hear or things that are read to you.

Write down key words, ideas, or instructions.

Draw pictures to help explain new concepts and then explain the pictures.

Color code things.

Avoid distractions during study times.

Remember that you need to see things, not just hear things, to learn well.

Tactile

If you are a tactile learner, you learn by touching and doing. You understand and remember things through physical movement. You are a "hands-on" learner who prefers to touch, move, build, or draw what you learn, and you tend to learn better when some type of physical activity is involved. You need to be active and take frequent breaks, you often speak with your hands and with gestures, and you may have difficulty sitting still.

As a tactile learner, you like to take things apart and put things together, and you tend to find reasons to tinker or move around when you become bored. You may be very well coordinated and have good athletic ability. You can easily remember things that were done but may have difficulty remembering what you saw or heard in the process. You often communicate by touching, and you appreciate physically expressed forms of encouragement, such as a pat on the back.

Here are some things that tactile learners like you can do to learn better:

Participate in activities that involve touching, building, moving, or drawing.

Do lots of hands-on activities like completing art projects, taking walks, or acting out stories.

It's OK to chew gum, walk around, or rock in a chair while reading or studying.

Use flashcards and arrange them in groups to show relationships between ideas.

Trace words with your finger to learn spelling (finger spelling).

Take frequent breaks during reading or studying periods (frequent, but not long).

It's OK to tap a pencil, shake your foot, or hold on to something while learning.

Use a computer to reinforce learning through the sense of touch.

Remember that you learn best by doing, not just by reading, seeing, or hearing.

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What's Your Learning Style? 20 Questions

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Auditory If you are an auditory learner, you learn by hearing and listening. You understand and remember things you have heard. You store information by the way it sounds, and you have an easier time understanding spoken instructions than written ones.

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CBSE Class 10 - Pair of linear Equations (in Punjabi) Offered by Unacademy

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Get access to the latest Pair of linear Equations (in Punjabi) prepared with CBSE Class 10 course curated by Bhawna Sharma on Unacademy to prepare for the toughest competitive exam.

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Intro to slope | Algebra (video) | Khan Academy

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Sal shows how to find the slope of a line.

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Graph and find a solution for the linear equation y=3x+2.

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Summative Assessment Option 1: Linear Equation Exam

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Summative Assessment Option 1: Linear Equation Exam

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Free open source NOTES, VIDEOS, and STEPS. Math for solving and simplifying linear, quadratic, polynomial and rational expressions and equations.

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Graphs of The Galaxy | Graphing Linear Equations | Online Math Resource

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Graphs of The Galaxy - Graphing Linear Equations. Online Math Resource. Match linear equations to blast space debris out of the path of your intergalactic mission - with your spacecraft laser of course!

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Interactive Slope, HTML5 Applet. Just Click, drag and Explore Graph and Formula of Slope

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Explore the slope formula with our interactive HTML5 applet. Shows rise, run and other features of the slope of a line

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Roof Slope | Real-Life Construction Math Lesson

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Slope Word Problem - Real Life Engineering Application | Eat Pi

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There are various applications of linear equations in Mathematics as well as in real life. An algebraic equation is an equality that includes variables and equal sign (=). A linear equation is an equation of degree one.

The knowledge of mathematics is frequently applied through word problems, and the applications of linear equations are observed on a wide scale to solve such word problems. Here, we are going to discuss the linear equation applications and how to use them in the real world with the help of an example.

What is Linear Equation?

A linear equation is an algebraic expression with a variable and equality sign (=), whose highest degree is equal to 1. For example, 2x - 1 = 5 is a linear equation.

A linear equation with one variable and degree one is called a linear equation in one variable. (Eg, 3x + 5 = 0)

A linear equation with degrees one and two variables is called a linear equation in two variables. (Eg, 3x + 5y = 0)

The graphical representation of linear equation is ax + by + c = 0, where,

a and b are coefficients

x and y are variables

c is a constant term

What are the Applications of Linear Equations?

In real life, the applications of linear equations are vast. To tackle real-life problems using algebra, we convert the given situation into mathematical statements in such a way that it clearly illustrates the relationship between the unknowns (variables) and the information provided. The following steps are involved while restating a situation into a mathematical statement:

Translate the problem statement into a mathematical statement and set it up in the form of algebraic expression in a manner it illustrates the problem aptly.

Identify the unknowns in the problem and assign variables (quantity whose value can change depending upon the mathematical context) to these unknown quantities.

Read the problem thoroughly multiple times and cite the data, phrases and keywords. Organize the information obtained sequentially.

Frame an equation with the help of the algebraic expression and the data provided in the problem statement and solve it using systematic techniques of equation solving.

Retrace your solution to the problem statement and analyze if it suits the criterion of the problem.

There you go!! Using these steps and applications of linear equations word problems can be solved easily.

Applications of Linear equations in Real life

Finding unknown age

Finding unknown angles in geometry

For calculation of speed, distance or time

Problems based on force and pressure

Let us look into an example to analyze the applications of linear equations in depth.

Applications of Linear Equations Solved Example
Example:
Rishi is twice as old as Vani. 10 years ago his age was thrice of Vani. Find their present ages.
Solution:
In this word problem, the ages of Rishi and Vani are unknown quantities. Therefore as discussed above, let us first choose variables for the unknowns.

Let us assume that Vani's present age is 'x' years. Since Rishi's present age is 2 times that of Vani, therefore his present age can be assumed to be '2x'.

10 years ago, Vani's age would have been 'x - 10 ', and Rishi's age would have been '2x - 10'. According to the problem statement, 10 years ago, Rishi's age was thrice of Vani, i.e. 2x - 10 = 3(x - 10).

We have our linear equation in the variable 'x' which clearly defines the problem statement. Now we can solve this linear equation easily and get the result.

This implies that the current age of Vani is 20 years, and Rishi's age is '2x,' i.e. 40 years. Let us retrace our solution. If the present age of Vani is 20 years then 10 years ago her age would have been 10 years, and Rishi's age would have been 30 years which satisfies our problem statement. Thus, applications of linear equations enable us to tackle such real-world problems.

Video Lesson on Applications of Linear Equation

Related Articles

Frequently Asked Questions - FAQs

What is the linear equation?

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a variable.
For example, ax + b = 0, where a and b are constants and a ≠ 0.

What are the applications of Linear equations in real life?

The applications of linear equations in real life are:
Finding unknown age
Finding unknown angles in geometry
For calculation of speed, distance or time
Problems based on force and pressure

What is a linear equation with one variable?

A linear equation with one variable and degree one is called a linear equation in one variable. (Eg, 3x + 5 = 0)

What is a linear equation with two variables?

A linear equation with degrees one and two variables is called a linear equation in two variables. (Eg, 3x + 5y = 0)

What is a graphical representation of a linear equation?

The graphical representation of linear equation is ax + by + c = 0,
Where,
a and b are coefficients
x and y are variables
c is a constant term

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Applications of Linear Equations in Maths and Real Life | Examples

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Application of linear equations can be seen in Maths and in real life as well. It is used to solve age problems, calculate speed, distance, time, etc. Learn about application of linear equations and how is algebra helpful in solving real life problems at BYJU'S.

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1. Write and solve a linear equation

2. Categorize and justify a linear equation as having a unique solution, no solution, or infinitely many solutions.

3. Plot solutions of a linear equation on the coordinate plane.

4. Graph a linear equation.

5. Define slope of a line as the rate of change of that line.

6. Solve systems of linear equations by substitution and elimination.

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1. slope

2. y-intercept

3. x-intercept

4. linear equation

5. constant speed

6. horizontal line

7. vertical line

8. linear equation

9. point-slope equation of a line

10. slope-intercept equation of a line

11. standard form of a linear equation

12. system of linear equations

13. solution to a system of linear equations

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Determine the slope and y intercept from an equation in standard form

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How to find the slope between two points

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How to plot points on a coordinate plane

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How to plot points on a coordinate plane

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Plotting Points on a Coordinate Plane | All 4 Quadrants

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线性方程也称一次方程式。指 未知数都是一次的方程。其一般的形式是ax+by+...+cz+d=0。线性方程的本质是等式两边乘以任何相同的非零数，方程的本质都不受影响。 [1]

因为在 笛卡尔坐标系上任何一个一次方程的表示都是一条 直线。组成一次方程的每个项必须是 常数或者是一个常数和一个 变量的乘积。且方程中必须包含一个变量，因为如果没有变量只有常数的式子是 代数式而非 方程式 。

线性方程也称为一次方程，因为在 笛卡尔坐标系上任何一个一次方程的表示都是一条直线。组成一次方程的每个项必须是 常数或者是一个常数和一个变量的乘积。且方程中必须包含一个变量，因为如果没有变量只有常数的式子是算数式而非 方程式 。

如果一个一次方程中只包含一个变量（x），那么该方程就是一元一次方程。如果包含两个变量（x和y），那么就是一个二元一次方程，以此类推。

一元一次方程式是指一个方程式中仅含有一个 变量，且等号两边至少有一个一次 单项式的方程。 [2]

形为 ax+by+...+cz+d=0 ，关于x、y的线性方程，是指经过整理后能变形为ax+by+c=0的方程（其中a、b、c为已知数，a、b不同时为0）。一元线性方程是最简单的方程，其形式为ax=b。因为把 一次方程在 坐标系 中表示出来的图形是一条直线，故称其为线性方程。

求解 二元一次联立方程式可以使用代入消去法或加减消去法。 [1]

代入消去法就是先利用其中一个方程，将含有其中一个未知数的代数式表示另一个未知数。然后代入另一个方程，从而将这组方程转化成解两个一元一次方程式的方法。

加减消去法就是将两个方程加或相减，从而消去其中一个未知数的方法。

通常，我们先将其中一个方程的两边同时乘以一个不是0的数，使其中的一个系数与另外一个方程的对应系数相同。再将两个方程相加或相减。

在例子中（不是特例）变量 y是 x 的函数，而且函数和方程的图像一致。

y=f(x)
一个函数如果满足这样的特性就叫做 线性函数，或者更一般的，叫 线性化 。

因为线性的独特属性，在同类方程中对线性函数的解决有 叠加 作用。这使得线性方程最容易解决和推演。

线性方程在应用数学中有重要规律。使用它们建立模型很容易，而且在某些情况下可以假设变量的变动非常小，这样许多 非线性 方程就转化为线性方程。

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线性方程也称一次方程式。指 未知数都是一次的方程。其一般的形式是ax+by+...+cz+d=0。线性方程的本质是等式两边乘以任何相同的非零数，方程的本质都不受影响。 [1] 因为在 笛卡尔坐标系上任何一个一次方程的表示都是一条 直线。组成一次方程的每个项必须是 常数或者是一个常数和一个 变量的乘积。且方程中必须包含一个变量，因为如果没有变量只有常数的式子是 代数式而非 方程式 。 线性方程也称为一次方程，因为在 笛卡尔坐标系上任何一个一次方程的表示都是一条直线。组成一次方程的每个项必须是 常数或者是一个常数和一个变量的乘积。且方程中必须包含一个变量，因为如果没有变量只有常数的式子是算数式而非 方程式 。 如果一个一次方程中只包含一个变量（x），那么该方程就是一元一次方程。如果包含两个变量（x和y），那么就是一个二元一次方程，以此类推。 一元一次方程式是指一个方程式中仅含有一个 变量，且等号两边至少有一个一次 单项式的方程。 [2] 形为 ax+by+...+cz+d=0 ，关于x、y的线性方程，是指经过整理后能变形为ax+by+c=0的方程（其中a、b、c为已知数，a、b不同时为0）。一元线性方程是最简单的方程，其形式为ax=b。因为把 一次方程在 坐标系 中表示出来的图形是一条直线，故称其为线性方程。 求解 二元一次联立方程式可以使用代入消去法或加减消去法。 [1] 代入消去法就是先利用其中一个方程，将含有其中一个未知数的代数式表示另一个未知数。然后代入另一个方程，从而将这组方程转化成解两个一元一次方程式的方法。 加减消去法就是将两个方程加或相减，从而消去其中一个未知数的方法。 通常，我们先将其中一个方程的两边同时乘以一个不是0的数，使其中的一个系数与另外一个方程的对应系数相同。再将两个方程相加或相减。 在例子中（不是特例）变量 y是 x 的函数，而且函数和方程的图像一致。 y=f(x) 一个函数如果满足这样的特性就叫做 线性函数，或者更一般的，叫 线性化 。 因为线性的独特属性，在同类方程中对线性函数的解决有 叠加 作用。这使得线性方程最容易解决和推演。 线性方程在应用数学中有重要规律。使用它们建立模型很容易，而且在某些情况下可以假设变量的变动非常小，这样许多 非线性 方程就转化为线性方程。

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Convertiendo ecuaciones a slope intercept form

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Convertiendo ecuaciones a slope intercept form

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Converting to Slope Intercept Form (Spanish Version)

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Como calcular el slope de una ecuacion lineal

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Como calcular el slope de una ecuacion lineal

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5 Slope-Intercept Form Using b and m (Spanish Version)

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Solutions to Systems of Linear Equations

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This activity will help students understand what it means for a point to be a solution to a system of equations - both graphically and algebraically. Translated by volunteers into: Arabic: https://teacher.desmos.com/activitybuilder/custom/5f56c2662378546a1f80434f French: https://teacher.desmos.com/activitybuilder/custom/59244d46e48c7f061336e00b

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8.EE.C.7
Domain: Expressions & Equations
Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations.
Standard: Solve linear equations in one variable.

8.EE.B.5
Domain: Expressions & Equations
Cluster: Understand the connections between proportional relationships, lines, and linear equations.
Standard: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

8.EE.B.6
Domain: Expressions & Equations
Cluster: Understand the connections between proportional relationships, lines, and linear equations.
Standard: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

8.EE.C.8
Domain: Expressions & Equations
Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations.
Standard: Analyze and solve pairs of simultaneous linear equations.

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How To Find The X and Y Intercepts of a Line

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A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

What is a Linear Equation?

An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has a variable whose exponent is more than 1. The graph of a linear equation always forms a straight line.

Linear Equation Definition: A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear' equation.

There are linear equations in one variable and linear equations in two variables. Let us learn how to identify linear equations and non-linear equations with the help of the following examples.

Linear Equation Formula

The linear equation formula is the way of expressing a linear equation. This can be done in different ways. For example, a linear equation can be expressed in the standard form, the slope-intercept form, or the point-slope form. Now, if we take the standard form of a linear equation, let us learn the way in which it is expressed. We can see that it varies from case to case based on the number of variables and it should be remembered that the highest (and the only) degree of all variables in the equation should be 1.

Slope intercept form of a linear equation is y = mx + c (where m = slope and c = y-intercept)

Point slope form of a linear equation is y - y₁ = m(x - x₁) (where m = slope and (x₁, y₁) is a point on the line)

Note: The slope of a linear equation is the amount by which the line is rising or falling. It is calculated by the formula rise/run. i.e., if (x ₁, y ₁) and (x ₂, y ₂) are any two points on a line then its slope is calculated using the formula (y ₂ - y ₁)/(x ₂ - x ₁).

Linear Equations in Standard Form

The standard form or the general form of linear equations in one variable is written as, Ax + B = 0; where A and B are real numbers, and x is the single variable. The standard form of linear equations in two variables is expressed as, Ax + By = C; where A, B and C are any real numbers, and x and y are the variables.

Linear Equation Graph

The graph of a linear equation in one variable x forms a vertical line that is parallel to the y-axis and vice-versa, whereas, the graph of a linear equation in two variables x and y forms a straight line. Let us graph a linear equation in two variables with the help of the following example.

Example: Plot a graph for a linear equation in two variables, x - 2y = 2.

Let us plot the linear equation graph using the following steps.

Step 1: The given linear equation is x - 2y = 2.

Step 2: Convert the equation in the form of y = mx + b. This will give: y = x/2 - 1.

Step 3: Now, we can replace the value of x for different numbers and get the resulting value of y to create the coordinates.

Step 4: When we put x = 0 in the equation, we get y = 0/2 - 1, i.e. y = -1. Similarly, if we substitute the value of x as 2 in the equation, y = x/2 - 1, we get y = 0.

Step 5: If we substitute the value of x as 4, we get y = 1. The value of x = -2 gives the value of y = -2. Now, these pairs of values of (x, y) satisfy the given linear equation y = x/2 - 1. Therefore, we list the coordinates as shown in the following table.

Step 6: Finally, we plot these points (4,1), (2,0), (0,-1) and (-2, -2) on a graph and join the points to get a straight line. This is how a linear equation is represented on a graph.

Linear Equations in One Variable

A linear equation in one variable is an equation in which there is only one variable present. It is of the form Ax + B = 0, where A and B are any two real numbers and x is an unknown variable that has only one solution. It is the easiest way to represent a mathematical statement. This equation has a degree that is always equal to 1. A linear equation in one variable can be solved very easily. The variables are separated and brought to one side of the equation and the constants are combined and brought to the other side of the equation, to get the value of the unknown variable.

Example: Solve the linear equation in one variable: 3x + 6 = 18.

In order to solve the given equation, we bring the numbers on the right-hand side of the equation and we keep the variable on the left-hand side. This means, 3x = 18 - 6. Then, as we solve for x, we get, 3x = 12. Finally, the value of x = 12/3 = 4.
☛Also check:
Linear Equations in Two Variables

A linear equation in two variables is of the form Ax + By + C = 0, in which A, B, C are real numbers and x and y are the two variables, each with a degree of 1. If we consider two such linear equations, they are called simultaneous linear equations. For example, 6x + 2y + 9 = 0 is a linear equation in two variables. There are various ways of solving linear equations in two variables like the graphical method, the substitution method, the cross multiplication method, the elimination method, and the determinant method.

☛Also check: Linear Equations In Two Variables Worksheets

How to Solve Linear Equations?

An equation is like a weighing balance with equal weights on both sides. If we add or subtract the same number from both sides of an equation, it still holds true. Similarly, if we multiply or divide the same number on both sides of an equation, it is correct. We bring the variables to one side of the equation and the constant to the other side and then find the value of the unknown variable. This is the way to solve a linear equation with one variable. Let us understand this with the help of an example.

Example: Solve the equation, 3x - 2 = 4.

We perform mathematical operations on the Left-hand side (LHS) and the right-hand side (RHS) so that the balance is not disturbed. So, let us add 2 on both sides to reduce the LHS to 3x. This will not disturb the balance. The new LHS is 3x - 2 + 2 = 3x and the new RHS is 4 + 2 = 6. Now, let us divide both sides by 3 to reduce the LHS to x. Thus, we have x = 2. This is one of the ways of solving linear equations in one variable.
Tips on Linear Equations:

The value of the variable that makes a linear equation true is called the solution or root of the linear equation.

The solution of a linear equation is unaffected if the same number is added, subtracted, multiplied, or divided into both sides of the equation.

The graph of a linear equation in one or two variables always forms a straight line.

☛ Related Articles:
Linear Equation Examples
Book a Free Trial Class
FAQs on Linear Equation

What is a Linear Equation? Explain with an Example.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. When this equation is graphed, it always results in a straight line. This is the reason why it is termed as a 'linear equation'. There are linear equations in one variable, in two variables, in three variables, and so on. A few examples of linear equations are 5x + 6 = 1, 42x + 32y = 60, 7x = 84, etc.

What is the Formula for a Linear Equation?

The formula for a linear equation is the way in which a linear equation is expressed. It can be expressed in the standard form, the slope-intercept form or the point-slope form. Using the slope-intercept form, the linear equation can be found using y = mx + c and using the point-slope form, it can be found using y - y ₁ = m(x-x ₁), where m is the slope, c is the y-intercept, and (x ₁, y ₁) is a point on the line.

Why is a Linear Equation Called Linear?

A linear equation is called linear because when we try to plot the graph of the given linear function, it results in a straight line.

How do you Solve Linear Equations?

We can solve a linear equation in one variable by moving the variables to one side of the equation, and the numeric part on the other side. For example, x - 1 = 5 - 2x can be solved by moving the numeric parts on the right-hand side of the equation, while keeping the variables on the left side. Hence, we get x + 2x = 5 + 1. Thus, 3x = 6. This gives x = 2.

Can Linear Equations have Fractions?

Yes, linear equations can have fractions only as long as the denominator in the fractional part is a constant value. The variables cannot be a part of the denominator of any fraction in a linear equation.

What are Linear Equations in One Variable?

A linear equation in one variable is an equation in which there is only one variable present. It is of the form Ax + B = 0, where A and B are any two real numbers and x is an unknown variable that has only one solution. For example, 9x + 78 = 18 is a linear equation in one variable.

How do You Convert a Linear Equation to Standard Form?

To convert a linear equation to standard form, you need to move all the variables to one side of the equation and the constants to the other side, and then rearrange the terms so that the variables are on the left side and the constant is on the right side.

What are Linear Equations in two Variables?

A linear equation in two variables is of the form Ax + By + C = 0, in which A and B are the coefficients, C is a constant term, and x and y are the two variables, each with a degree of 1. For example, 7x + 9y + 4 = 0 is a linear equation in two variables. If we consider two such linear equations, they are called simultaneous linear equations.

How are Quadratic Equations Different from Linear Equations?

Linear equations do not have any exponent other than 1 in any term. The general form of a linear equation is expressed as Ax + By + C = 0, where A, B, and C are any real numbers and x and y are the variables. Whereas, quadratic equations have at least one term containing a variable that is raised to the second power. The general form of a quadratic equation is expressed as ax ² + bx + c = 0. Another difference between the two types of equations is that a linear equation forms a straight line whereas a quadratic equation forms a parabola on the graph.

How to Graph Linear Equations?

When we graph linear equations, it forms a straight line. In order to graph an equation of the form, Ax + By = C, we get two solutions that are corresponding to the x-intercepts and the y-intercepts. We convert the equation to the form, y = mx + b. Then, we replace the value of x with different numbers and get the value of y which creates a set of (x,y) coordinates. These coordinates can be plotted on the graph and then joined by a line.

How to Solve Linear Equations with Fractions?

Linear equations with fractions are solved in the same way as we solve the usual equations. We need to bring the variable on one side and the constants on the other side and solve for the variable. For example, let us solve the equation (2a/3) - 10 = 12.

Step 1: Here, we will bring the constants on the right-hand side, i.e., (2a/3) = 12 + 10.

Step 2: Now, we have (2a/3) = 22. This can be further written as, 2a = 22 × 3.

Step 3: Therefore, the value of a = 66/2 = 33.

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Linear Equations - Definition, Formula, Graph, Examples

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A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0.

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1. Create a linear equation describing something that shows up in your life.

2. Describe the process of graphing an equation using a mix of different languages

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1. Define slope and explain the process of finding the slope in home language

2. Use content terms slope, linear equation, and system of linear equations.

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1. Use cognates in mathematics related to solving linear equations (negative, positive, multiply, divide, products, sum, etc.)

2. Use google translate to translate directions and information

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Forms of linear equations review (article) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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A system of equations is two or more equations that contain the same variables. A solutions to a system of equations are the point where the lines intersect. There are four methods to solving systems of equations: graphing, substitution, elimination and matrices. Solving systems of equations is an important concept that shows up first in Algebra I, but is built upon in upper-level math.

Solving systems of equations is a really really important skill in all of your Math classes. It shows up for the first in Algebra one but it continues in pretty much every course thereafter. So this is a really important idea that you're going to want to focus on in your first time through.
A system of equations is two or more equations that contain the same variables.
In Algebra class you'll probably only seen see two variables that are both raised to the first power but when you get into advanced Algebra or about Algebra two, you might start seeing things with x squared, y squared sometimes you have three or even four equations not just x and y but xyz and w or something like that but for Algebra most of the time we're just talking about two equations that have x and y in both of them.
The solution to a systems of equations, is the solution in both or all original equations. It's the point where the lines intersect. What that means is that if I take my x and y pair that I think is the solution and I substitute them into both original equations, both original equations will come out true they'll come out as equalities that's how I'll know if my work is correct. The other way I could check my work is by doing a graph and see if my solution point is where the lines cross. You'll get into that a lot once you start doing some practice problems. When you're asked to solve these, there's four methods that are commonly used.
The first method is to graph, you graph both lines see where they cross and that's your solution point. If you're not a good grapher don't worry there is other options for you. Substitution is where you get one variable isolated by itself and then substitute that expression into the other equation. That's what Substitution looks like and it's really commonly used when you have equations that are both in y=mx+b form.
A third method is called Elimination and that's where you look at the coefficients in front of x and y and you try to get coefficients in your two equations that are additive inverses. So like if my equation one has 3x+4y or something I want my equation two to have -3x, that way when I work with the equations together my positive 3x and -3x would be eliminated when I added them together. That's what an additive inverse is.
The fourth method is something that you don't see until you're more advanced in Math classes probably not until you're advanced Algebra or Algebra two class. So I'm going to cross that off we're not going to be going over that in Algebra one course but you will see that in your future.
So if you're a good grapher, this might be the one you choose, if you're good at using Algebra like you're pretty accurate when you write out all your Math homework and you don't lose negative signs you're pretty good with fractions and stuff like that Substitution or Elimination might be your favorite method. However, it's best to know how to do all the methods so that in case you get to your Math test and you have like a brain fart and you forget how to do Substitution, you're still able to use either Elimination or Graphing.

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Introduction to Systems of Equations - Concept - Algebra Video by Brightstorm

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A system of equations is two or more equations that contain the same variables. A solutions to a system of equations are the point where the lines intersect. There are four methods to solving systems of equations: graphing, substitution, elimination and matrices.

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Summative Assessment Option 2: Project - Build a Dog House

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Summative Assessment Option 2: Project - Build a Dog House