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When solving equations, always follow PEMDAS:
Parentheses
Exponents
Multiplication and Division (left to right)
Addition and Subtraction (left to right)

This order is crucial when solving complex equations!

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Today we'll be going over topic  MA.912.AR.9.1:

Write and solve a system of linear equations in real world context. We'll be learning how to write and solve systems of linear equations using these real-world scenarios as well as the different forms of linear equations. We'll also be learning how to apply PEMDAS to the process.

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Systems of linear equations are everywhere! From calculating cell phone plans to determining the best deal at the grocery store. This skill helps you make informed decisions in everyday life and prepare for careers in business, engineering, and science.

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Basic formula:

y - y1 = m(x - x1)

https://images.app.goo.gl/P9Pw7ntNujqR9zJm6

Here's a video to help you better understand it:

Point Slope Form - Basic Introduction - Algebra

https://youtu.be/yoHs1h5qtuQ?si=RFy5jItvZ7D3MDXb

How would the formula look if you had a 6 for y and a 4 for x?

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Basic formula:

y = mx + b

Here's a video to help you better understand it:

Converting Linear Equations from Standard Form to Slope Intercept Form

https://youtu.be/4WktSA13vKc?si=2w1B-cYlbp7M_X92

How would the formula look if you had a 7 for x and a 2 for b?

Creative example:
Let x = number of adult tickets
Let y = number of child tickets

Equation 1: x + y = 200 (total tickets)
Equation 2: 12x + 8y = 2160 (total revenue)

Remember: Write equations in standard form!

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How to write the system of equations from a word problem

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A coffee shop sells lattes for $4 and cappuccinos for $3.50. On Monday, they sold 100 drinks total and made $375. How many of each drink did they sell?

Try solving this using either method! Remember to:
1. Define variables
2. Write equations
3. Solve systematically using PEMDAS
4. Check your answer

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Ready for more practice? Check out these great resources:
- Khan Academy: Systems of Equations
- IXL Math: Linear Systems
- Desmos Activities
- Open Middle Problems

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Systems of equations | Algebra basics | Math | Khan Academy

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Basic formula:

Ax + By = C

How would the formula look if you had a 1.5 for y and a 3 for x?

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How to Convert Number into Standard Form (Part 2/4)  #24

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Even as we look around us in the real world, objects and architecture are made of linear lines.

These lines can be expressed and rearranged into the many forms we've gone over.

Ex: A line going from the corner of one block to the corner of another can be expressed as going right 3 (x) and going up 2 (y) so it can be expressed as:

A3 + B2 = C

or

2 = m3 + b

Looking at the following Picture above how can linear lines on this chess board be created?

Imagine how a linear line can go from the bottom left corner of H1 to the top right corner of 6A

Write a slope intercept equation that would go from H1 to D3

Write a slope intercept equation that would go from H1 to A8

Write a slope intercept equation that would go from E1 to H4

Write a slope intercept equation that would go from G1 to A4

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Printable Chess Boards And Pieces PDF - Free Printables

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Download free printable chess boards and pieces templates. Our printable chess set includes a playing board and two sets of pieces.

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Steps:
1. Solve one equation for one variable
2. Substitute that expression into the other equation
3. Solve for the remaining variable
4. Substitute back to find the first variable
5. Check your solution in both original equations

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Substitution Method to Solve a System of Equations

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Steps:
1. Align like terms
2. Multiply one or both equations to create opposite coefficients
3. Add equations to eliminate one variable
4. Solve for remaining variable
5. Substitute to find other variable
6. Check solution

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Solving a System of Equations Using Elimination and Multipliers