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Any equation which can be put in the form ax + by + c = 0, where a, b and c are real numbers, and a and b are not both zero, is called a linear equation in two variables. This means that you can think of many many such equations.

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A linear equation in two variables has a pair of numbers that can satisfy the equation. This pair of numbers is called as the solution of the linear equation in two variables. The solution can be found by assuming the value of one of the variables and proceeding to find the other solution.

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In a One-day International Cricket match between India and Australia played in Nagpur, two Indian batsmen together scored 176 runs, Express this information in the form of an equation.

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Ex 4.1, 1 - The cost of a notebook is twice cost of a pen

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Transcript

Ex 4.1, 1 The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. (Take the cost of a notebook to be Rs x and that of a pen to be Rs y.) Let the cost of a notebook be Rs x and the cost of pen be Rs y It is given that Cost of notebook = 2 Cost of pen x = 2y x 2y = 0 x 2y = 0 is the linear equation in two variables

1. Chapter 4 Class 9 Linear Equations in Two Variables

2. Serial order wise

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Ex 4.1, 1 - The cost of a notebook is twice cost of a pen

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Ex 4.1, 1 The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. (Take the cost of a notebook to be Rs x and that of a pen to be Rs y.)

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KSEEB Solutions for Class 9 Maths Chapter 10 Linear Equations in Two Variables Ex 10.2 - KSEEB Solutions

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KSEEB Solutions for Class 9 Maths Chapter 10 Linear Equations in Two Variables Ex 10.2 are part of KSEEB Solutions for Class 9 Maths. Here we have given Karnataka Board Class 9 Maths Chapter 10 Linear Equations in Two Variables Exercise 10.2.

Karnataka Board Class 9 Maths Chapter 10 Linear Equations in Two Variables Ex 10.2

Question 1.
Which one of the following options is true, and why ?
y = 3x + 5 has
i) a unique solution,
ii) only two solutions,
iii) infinitely many solutions.
Solution:
y = 3x + 5 has many solutions. Because this is a linear equation with two variables.

Question 3.
Check which of the following are solutions of the equation x - 2y = 4 and which are not:
i) (0, 2)
ii) (2, 0)
iii) (4, 0)
iv) (\(\sqrt{2}, 4 \sqrt{2}\))
v) (1, 1)
Solution:
i) (0, 2)
x - 2y = 4
0 - 2(2) = 4
0 - 4 = 4
-4 ≠ 4
∴ (0, 2) is not a solution.

iv)

Question 4.
Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k.
Solution:
2x + 3y = k
If x = 2, y = 1, then k = ?
2x + 3y = k
2(2) + 3(1) = k
4 + 3 = k
7 = k
∴ k = 7.

We hope the KSEEB Solutions for Class 9 Maths Chapter Linear Equations in Two Variables Ex 10.2 help you. If you have any query regarding Karnataka Board Class 9 Maths Chapter Linear Equations in Two Variables Exercise 10.2, drop a comment below and we will get back to you at the earliest.

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KSEEB Solutions for Class 9 Maths Chapter 10 Linear Equations in Two Variables Ex 10.2 - KSEEB Solutions

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KSEEB Solutions for Class 9 Maths Chapter 10 Linear Equations in Two Variables Ex 10.2 are part of KSEEB Solutions for Class 9 Maths. Here we have given Ka

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Linear Equations in 2 Variables 01 | Solution of Linear Equations | Class 9 | NCERT | Sprint

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Linear Equations in 2 Variables 01 | Solution of Linear Equations | Class 9 | NCERT | Sprint

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Class 9 Maths | Chapter 4 | Introduction Part 1 | Linear Equation in Two Variables | NCERT

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Class 9 Maths | Chapter 4 | Introduction Part 1 | Linear Equation in Two Variables | NCERT

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Linear equation in one variable has a unique solution. Then, what about the solution of a linear equation involving two variables? If there are two variables in the equation, a solution involves a pair of values, one for x and one for y which satisfy the given equation.

A linear equation is represented graphically by the line whose points give the collection of solutions of the equation. This is called the graph of a linear equation.

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KSEEB Solutions for Class 9 Maths Chapter 10 Linear Equations in Two Variables Ex 10.3

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KSEEB Solutions for Class 9 Maths Chapter 10 Linear Equations in Two Variables Ex 10.3

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KSEEB Solutions for Class 9 Maths Chapter 10 Linear Equations in Two Variables Ex 10.3 are part of KSEEB Solutions for Class 9 Maths. Here we have given Karnataka Board Class 9 Maths Chapter 10 Linear

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Definition:  The equation of a line parallel to x-axis is of the form y = b and it cuts the y-axis at the point (0, b). This line is parallel to x-axis and is at a perpendicular distance of 'b' units from the x-axis. The slope of the equation of line parallel to x-axis is zero, since it is parallel to the x-axis.

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Definition: The equation of a line parallel to y axis is of the form x = a and it cuts the x-axis at the point (a, 0). This line is parallel to y axis and is at a perpendicular distance of 'a' units from the y-axis. The slope of the equation of line parallel to y axis is undefined, since it is inclined at 90º with the x axis.

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KSEEB Solutions for Class 9 Maths Chapter 10 Linear Equations in Two Variables Ex 10.4

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KSEEB Solutions for Class 9 Maths Chapter 10 Linear Equations in Two Variables Ex 10.4

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KSEEB Solutions for Class 9 Maths Chapter 10 Linear Equations in Two Variables Ex 10.4 are part of KSEEB Solutions for Class 9 Maths. Here we have given Karnataka Board Class 9 Maths Chapter 10 Linear

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Class 9 Maths | Chapter 4 | Exercise 4.4 Q1 | Linear Equation in Two Variables | NCERT

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Class 9 Maths | Chapter 4 | Exercise 4.4 Q1 | Linear Equation in Two Variables | NCERT

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Class 9 Maths | Chapter 4 | Exercise 4.3 Q1 | Linear Equation in Two Variables | NCERT

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Class 9 Maths | Chapter 4 | Exercise 4.3 Q1 | Linear Equation in Two Variables | NCERT

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The topic of Linear Equations in Two Variables in mathematics has several values in teaching, both in terms of mathematical concepts and real-life applications.

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The subtopic Solution of Linear Equation gives the Value Equality Where finding solution for a variable is possible only if there exists an equation of equality between two terms. Similarly,only if equality among individuals prevail in an organisation or society,their potential can be understood.

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Solving linear equations in two variables requires multiple steps and iterative approaches, Teaching this topic encourages students to Preserve, stay organized and persist in their problem solving efforts that develpes a matured mindset.