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7.1E: Systems of Linear Equations - Two Variables (Exercises)

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For the following exercises, determine whether the ordered pair is a solution to the system of equations.

3 x-y=4

1. \quad and (-1,1) x+4 y=-3
6 x-2 y=24

2. -3 x+3 y=18

For the following exercises, use substitution to solve the system of equations.

3
10 x+5 y=-5
3 x-2 y=-12

4
\frac{4}{7} x+\frac{1}{5} y=\frac{43}{70}
\frac{5}{6} x-\frac{1}{3} y=-\frac{2}{3}

5

5 x+6 y=14
4 x+8 y=8

For the following exercises, use addition to solve the system of equations.

6
3 x+2 y=-7
2 x+4 y=6

7.

3 x+4 y=2
9 x+12 y=3

8.

8 x+4 y=2
6 x-5 y=0.7

For the following exercises, write a system of equations to solve each problem. Solve the system of equations.

9. A factory has a cost of production C(x)=150 x+15,000 and a revenue function R(x)=200 x. What is the break-even point?

10. A performer charges C(x)=50 x+10,000, where x is the total number of attendees at a show. The venue charges \$ 75 per ticket. After how many people buy tickets does the venue break even, and what is the value of the total tickets sold at that point?


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