## Engage NY Eureka Math 8th Grade Module 4 Lesson 12 Answer Key

### Eureka Math Grade 8 Module 4 Lesson 12 Opening Exercise Answer Key

Emily tells you that she scored 32 points in a basketball game. Write down all the possible ways she could have scored 32 with only two- and three-point baskets. 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.
2x+3y=32

### Eureka Math Grade 8 Module 4 Lesson 12 Exercise Answer Key

Exploratory Challenge/Exercises

Question 1.
Find five solutions for the linear equation x+y=3, and plot the solutions as points on a coordinate plane.   Question 2.
Find five solutions for the linear equation 2x-y=10, and plot the solutions as points on a coordinate plane.   Question 3.
Find five solutions for the linear equation x+5y=21, and plot the solutions as points on a coordinate plane.   Question 4.
Consider the linear equation $$\frac{2}{5}$$ x+y=11.
a. Will you choose to fix values for x or y? Explain.
If I fix values for x, it will make the computations easier. Solving for y can be done in one step.

b. Are there specific numbers that would make your computational work easier? Explain.
Values for x that are multiples of 5 will make the computations easier. When I multiply $$\frac{2}{5}$$ by a multiple of 5, I will get an integer.

c. Find five solutions to the linear equation $$\frac{2}{5}$$ x+y=11, and plot the solutions as points on a coordinate plane.
x Linear Equation:  Question 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, that you can buy with$35.
2x+y=35

b. Find five solutions to the linear equation from part (a), and plot the solutions as points on a coordinate plane.   ### Eureka Math Grade 8 Module 4 Lesson 12 Exit Ticket Answer Key

Question 1.
Is the point (1,3) a solution to the linear equation 5x-9y=32? Explain.
No, (1,3) is not a solution to 5x-9y=32 because 5(1)-9(3)=5-27=-22, and -22≠32.

Question 2.
Find three solutions for the linear equation 4x-3y=1, and plot the solutions as points on a coordinate plane.  ### Eureka Math Grade 8 Module 4 Lesson 12 Problem Set Answer Key

Students practice finding and graphing solutions for linear equations that are in standard form.

Question 1.
Consider the linear equation x-$$\frac{3}{2}$$ y=-2.
a. Will you choose to fix values for x or y? Explain.
If I fix values for y, it will make the computations easier. Solving for x can be done in one step.

b. Are there specific numbers that would make your computational work easier? Explain.
Values for y that are multiples of 2 will make the computations easier. When I multiply $$\frac{3}{2}$$ by a multiple of 2, I will get a whole number.

c. Find five solutions to the linear equation x-$$\frac{3}{2}$$ y=-2, and plot the solutions as points on a coordinate plane.   Question 2.
Find five solutions for the linear equation $$\frac{1}{3}$$ x+y=12, and plot the solutions as points on a coordinate plane.  Question 3.
Find five solutions for the linear equation -x+$$\frac{3}{4}$$ y=-6, and plot the solutions as points on a coordinate plane.  Question 4.
Find five solutions for the linear equation 2x+y=5, and plot the solutions as points on a coordinate plane.    