Question

In the following exercises, solve the following systems of equations by graphing.

$$\begin{gathered} y=x-2 \\ y=-3x+2 \end{gathered}$$

Short answer

The solution of the system of linear equations is (1,-1).

Step-by-step solution

Step 1. Given information

Two linear equations are

$$\begin{gathered} y=x-2 \\ y=-3x+2 \end{gathered}$$

Step 2. Solving equations for the intersection points 

First, solve both of these equations for y such that their slopes and y intercepts may be easily graphed.

And find the slope and y-intercept by solving the first equation for y

$$\begin{gathered} y=x-2 \\ \mathrm{Here}\mathrm{the}\mathrm{slope}\mathrm{is}m=1 \\ \mathrm{And}\mathrm{the}\mathrm{y}-\mathrm{intercept}\mathrm{is}b=-2 \end{gathered}$$

Again find the slope and y-intercept by solving the Second equation for y.

$$\begin{gathered} y=-3x+2 \\ \mathrm{Here}\mathrm{the}\mathrm{slope}\mathrm{is}m=-3 \\ \mathrm{And}\mathrm{the}y-\mathrm{intercept}\mathrm{is}b=2 \end{gathered}$$

Step 3. Graph obtained  

Step 4. Checking the values

$$\begin{gathered} \mathbf{Check}\mathbf{}\mathbf{:} \\ \mathrm{First}\mathrm{substitute}x=1, \\ y=-1\mathrm{into}\mathrm{the}\mathrm{equation} \\ y=x-2 \\ y=x-2 \\ -1=1-2 \\ -1=-1 \\ \mathrm{This}\mathrm{is}\mathrm{true}. \end{gathered}$$

$$\begin{gathered} \mathrm{Also}\mathrm{substitute}x=1, \\ y=-1 \\ \mathrm{into}\mathrm{the}\mathrm{equation}y=-3x+2 \\ y=-3x+2 \\ -1=-3\left(1\right)+2 \\ -1=-3+2 \\ -1=-1 \\ \mathrm{This}\mathrm{is}\mathrm{true}. \end{gathered}$$