System of Equations

Practice Questions

Algebra II › System of Equations

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1

When graphed, the lines represented in the system of equations below will intersect in which quadrant?

3x - 2y = 0

4x+3y = -17

2

When graphed, the lines represented in the system of equations below will intersect in which quadrant?

3x - 2y = 0

4x+3y = -17

3

Miles is a professional fitness instructor who will be teaching classes at a local gym. To get certified as an instructor, he spent a total of $400. Miles will be earning a base salary of $80 per month from the gym, plus an additional $20 for every class he teaches. If Miles teaches a certain number of classes during his first month as an instructor, he will earn back the amount he spent on certification. How many classes will that take?

Write a system of equations that models this situation, graph it, and type the solution.

4

Emeka is a professional fitness instructor who will be teaching classes at a local gym. To get certified as an instructor, he spent a total of $500. Emeka will be earning a base salary of $100 per month from the gym, plus an additional $20 for every class he teaches. If Emeka teaches a certain number of classes during his first month as an instructor, he will earn back the amount he spent on certification. How many classes will that take?

Write a system of equations that models this situation, graph it, and type the solution.

5

Alf and Tanner are having a workout competition. Whoever completes the most workouts in a month gets $25 from the other. Alf has already completed 4 workouts, whereas Tanner has finished 2 of them. Going forward, Alf has committed to completing 2 workouts per week, and Tanner has committed to completing 3 per week. At some point soon, the two friends will have completed the same number of workouts. How many workouts will that be?

Write a system of equations, graph them, and type the solution.

6

Miles is a professional fitness instructor who will be teaching classes at a local gym. To get certified as an instructor, he spent a total of $400. Miles will be earning a base salary of $80 per month from the gym, plus an additional $20 for every class he teaches. If Miles teaches a certain number of classes during his first month as an instructor, he will earn back the amount he spent on certification. How many classes will that take?

Write a system of equations that models this situation, graph it, and type the solution.

7

Emeka is a professional fitness instructor who will be teaching classes at a local gym. To get certified as an instructor, he spent a total of $500. Emeka will be earning a base salary of $100 per month from the gym, plus an additional $20 for every class he teaches. If Emeka teaches a certain number of classes during his first month as an instructor, he will earn back the amount he spent on certification. How many classes will that take?

Write a system of equations that models this situation, graph it, and type the solution.

8

Alf and Tanner are having a workout competition. Whoever completes the most workouts in a month gets $25 from the other. Alf has already completed 4 workouts, whereas Tanner has finished 2 of them. Going forward, Alf has committed to completing 2 workouts per week, and Tanner has committed to completing 3 per week. At some point soon, the two friends will have completed the same number of workouts. How many workouts will that be?

Write a system of equations, graph them, and type the solution.

9

This graph shows which of the following inequalities?

Screen shot 2020 06 23 at 10.11.20 pm

10

This graph shows which of the following inequalities?

Screen shot 2020 06 23 at 10.11.20 pm

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