# Lesson 15

Writing Systems of Equations

Let’s write systems of equations from real-world situations.

### Problem 1

Kiran and his cousin work during the summer for a landscaping company. Kiran's cousin has been working for the company longer, so his pay is 30% more than Kiran's. Last week his cousin worked 27 hours, and Kiran worked 23 hours. Together, they earned \$493.85. What is Kiran's hourly pay? Explain or show your reasoning.

### Problem 2

Decide which story can be represented by the system of equations $$y=x+6$$ and $$x+y=100$$. Explain your reasoning.

1. Diego’s teacher writes a test worth 100 points. There are 6 more multiple choice questions than short answer questions.
2. Lin and her younger cousin measure their heights. They notice that Lin is 6 inches taller, and their heights add up to exactly 100 inches.

### Problem 3

Clare and Noah play a game in which they earn the same number of points for each goal and lose the same number of points for each penalty. Clare makes 6 goals and 3 penalties, ending the game with 6 points. Noah earns 8 goals and 9 penalties and ends the game with $$\text-22$$ points.

1. Write a system of equations that describes Clare and Noah's outcomes. Use $$x$$ to represent the number of points for a goal and $$y$$ to represent the number of points for a penalty.

2. Solve the system. What does your solution mean?

### Problem 4

Solve: $$\begin{cases} y=6x-8 \\ y=\text-3x+10 \\ \end{cases}$$

(From Unit 4, Lesson 14.)

### Problem 5

1. Estimate the coordinates of the point where the two lines meet.

2. Choose two equations that make up the system represented by the graph.

1. $$y=\frac54x$$

2. $$y=6-2.5x$$

3. $$y=2.5x+6$$

4. $$y=6-3x$$

5. $$y=0.8x$$

3. Solve the system of equations and confirm the accuracy of your estimate.

(From Unit 4, Lesson 13.)