Lesson 15
Writing Systems of Equations
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.
Solution
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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.
Solution
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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.
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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.
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Solve the system. What does your solution mean?
Solution
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Problem 4
Solve: \(\begin{cases} y=6x-8 \\ y=\text-3x+10 \\ \end{cases}\)
Solution
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(From Unit 4, Lesson 14.)Problem 5
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Estimate the coordinates of the point where the two lines meet.
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Choose two equations that make up the system represented by the graph.
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\(y=\frac54x\)
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\(y=6-2.5x\)
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\(y=2.5x+6\)
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\(y=6-3x\)
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\(y=0.8x\)
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Solve the system of equations and confirm the accuracy of your estimate.
Solution
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(From Unit 4, Lesson 13.)