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?

Do not include units ($) in your answer.

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Explain or show your reasoning.

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

- 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.

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Explain your reasoning.

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 -22 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.

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Solve the system.

Write your answer in the following format:

(x,y)

with no spaces.

What does your solution mean?

Solve:

Write your answer in the following format:

(x,y)

with no spaces.

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

Write your answer in the following format:

(x,y)

with no spaces.

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

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

What is the x-value of the solution?

Give your answer as a simple fraction.

What is the y-value of the solution?

Give your answer as a simple fraction.