Lesson 15
Writing Systems of Equations
Let’s write systems of equations from realworld 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.
 Diego’s teacher writes a test worth 100 points. There are 6 more multiple choice questions than short answer questions.
 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 \(\text22\) points.

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.

Solve the system. What does your solution mean?
Problem 4
Solve: \(\begin{cases} y=6x8 \\ y=\text3x+10 \\ \end{cases}\)
Problem 5

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

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

\(y=\frac54x\)

\(y=62.5x\)

\(y=2.5x+6\)

\(y=63x\)

\(y=0.8x\)


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