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

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

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

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

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

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

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?