# 11.1E: 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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