 # Linear Equations in Two Variables

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Lesson Plans and Worksheets for Grade 8
Lesson Plans and Worksheets for all Grades

Examples, videos and solutions to help Grade 8 students learn how to solve linear equations with two variables.

### New York State Common Core Math Grade 8, Module 4, Lesson 12

Common Core Math Grade 8, Module 4, Lesson 12 Worksheets (pdf)

### Lesson 12 Outcome

• Students use a table to find solutions to a given linear equation and plot the solutions on a coordinate plane.

### Lesson 12 Summary

• A two-variable linear equation in the form ax + by = c is said to be in standard form.
• A solution to a linear equation in two variables is the ordered pair (x, y) that makes the given equation true. Solutions can be found by fixing a number for x and solving for y or fixing a number for y and solving for x.

Opening Exercise
Emily tells you that she scored 32 points in a basketball game with only two- and three-point baskets (no free throws).
How many of each type of basket did she score? Use the table below to organize your work.
Let x be the number of two-pointers and y be the number of three-pointers that Emily scored. Write an equation to represent the situation.

Exploratory Challenge/Exercises 1–5
1. Find five solutions for the linear equation x + y = 3, and plot the solutions as points on a coordinate plane.
2. Find five solutions for the linear equation 2x - y = 10, and plot the solutions as points on a coordinate plane.
3. Find five solutions for the linear equation x + 5y = 21, and plot the solutions as points on a coordinate plane.
4. Consider the linear equation 2/5x + y = 11.
a. Will you choose to fix values for x or y? Explain.
b. Are there specific numbers that would make your computational work easier? Explain.
c. Find five solutions to the linear equation 2/5x + y = 11, and plot the solutions as points on a coordinate plane.
5. At the store you see that you can buy a bag of candy for \$2 and a drink for \$1. Assume you have a total of \$35 to spend. You are feeling generous and want to buy some snacks for you and your friends.
a. Write an equation in standard form to represent the number of bags of candy, x, and the number of drinks, y, you can buy with \$35.
b. Find five solutions to the linear equation, and plot the solutions as points on a coordinate plane.

### NYS Math Module 4 Grade 8 Lesson 12 Exercises

1. Find five solutions for the linear equation 2x = y - 4, and plot the solutions as points on a coordinate plane.

2. Find five solutions for the linear equation 3x + y = 15, and plot the solutions as points on a coordinate plane.

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