A contracting company rents a generator for 6 hours and a heavy-duty saw for 6 hours at a total cost of 48 dollars. For another job the company rents the generator for 4 hours and the saw for 8 hours for a total cost of 40 dollars. Find the hourly rates $g$ (for the generator) and $s$ (for the saw) by solving the system of equations $6 g+6 s=48$ and $4 g+8 s=40$.

Name the variable you would solve for first. Explain.

$$\begin{aligned} & x-3 y=0 \\ & x-2 y=10 \end{aligned}$$

Graph the system of linear inequalities.

$$\begin{aligned} x & \geq 0 \\ y & \geq 0 \\ 2 x+3 y & \leq 12 \end{aligned}$$

Estimate the solution of the linear system graphically. Then check the solution algebraically.

$$\begin{array}{r} 4 x-y=10 \\ -2 x+4 y=16 \end{array}$$

Use any method to solve the linear system and tell how many solutions the system has.

$$\begin{aligned} & 3 x+2 y=12 \\ & 9 x+6 y=18 \end{aligned}$$

What is the solution of the following linear system?

$$\begin{aligned} -2 x+7 y & =-3 \\ x-7 y & =-2 \end{aligned}$$

(A) 1

(B) 5

(C) (1,5)

(D) (5,1)

Estimate the solution of the linear system graphically. Then check the solution algebraically.

$$\begin{aligned} x+9 y & =9 \\ 3 x+6 y & =6 \end{aligned}$$

Use the graph-and-check method to solve the linear system.

$$\begin{aligned} & x-y=-2 \\ & x+y=-4 \end{aligned}$$

Solve the linear system. Then check your solution.

$$\begin{aligned} 5 x+2 y & =-4 \\ -5 x+3 y & =19 \end{aligned}$$

Find the volume of the geometric figure shown.

Estimate the solution of the linear system graphically. Then check the solution algebraically.

$$\begin{aligned} 2 x+3 y & =36 \\ -2 x+y & =-4\end{aligned}$$

Describe the graph of a linear system that has the given number of solutions. Sketch an example.

Exactly one solution

Choose a method to solve the linear system. Explain your choice.

$$\begin{aligned} & 3 x+5 y=25 \\ & 2 x-6 y=12 \end{aligned}$$

In Exercises 2 and 3, find and correct the error.