Lesson 16

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 5, Lesson 15.)

Problem 5

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

    Graph of two intersecting lines in the xy-plane.
  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 5, Lesson 14.)