Question

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

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

Short answer

The solution to the linear equations is (0,2).

Step-by-step solution

Step 1. Given information 

The given linear equations are

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

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.

$$\begin{gathered} y=x+2 \\ \mathrm{Here}\mathrm{the}\mathrm{slope}\mathrm{is}m=1 \\ \mathrm{And}\mathrm{the}\mathrm{y}-\mathrm{intercept}\mathrm{is}b=2 \\ \mathrm{Again}\mathrm{Solve}\mathrm{the}\mathrm{second}\mathrm{equation}\mathrm{for}\mathrm{y},\mathrm{and}\mathrm{find}\mathrm{the}\mathrm{slope}\mathrm{and}\mathrm{y}-\mathrm{intercept}. \\ y=-2x+2 \\ \mathrm{Here}\mathrm{the}\mathrm{slope}\mathrm{is}m=-2 \\ \mathrm{And}\mathrm{the}\mathrm{y}-\mathrm{intercept}\mathrm{is}b=2 \end{gathered}$$

Step 3. Graph obtained 

Step 4. Checking the equation

$$\begin{gathered} \mathrm{Check}: \\ \mathrm{First}\mathrm{substitute}x=0, \\ y=2\mathrm{Into}\mathrm{the}\mathrm{equation} \\ y=x+2. \\ y=x+2 \\ 2=0+2 \\ 2=2 \\ \mathrm{This}\mathrm{is}\mathrm{true}. \\ \mathrm{Also}\mathrm{substitute}x=0, \\ y=2\mathrm{into}\mathrm{the}\mathrm{equation} \\ y=-2x+2 \\ y=-2x+2 \\ 2=-2\left(0\right)+2 \\ 2=0+2 \\ 2=2 \\ \mathrm{This}\mathrm{is}\mathrm{true}. \\ \mathrm{The}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{system}\mathrm{of}\mathrm{linear}\mathrm{equations}\mathrm{is}(0,2) \end{gathered}$$