6.2E: Systems of Linear Equations - Two Variables (Exercises)

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?