Question

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

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

Short answer

The solution of the system of linear equations is (-2,-2).

Step-by-step solution

Step 1. 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.

$$\begin{gathered} x+y=-4 \\ y=-x-4 \\ \mathrm{Here}\mathrm{the}\mathrm{slope}\mathrm{is}m=-1 \\ \mathrm{And}\mathrm{the}\mathrm{y}-\mathrm{intercept}\mathrm{is}b=-4 \end{gathered}$$

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

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

Step 2. Graph obtained

Step 3. Checking the equations

$$\begin{gathered} \mathrm{Check}: \\ \mathrm{First}\mathrm{substitute}x=-2, \\ y=-2\mathrm{into}\mathrm{the}\mathrm{equation} \\ x+y=-4 \\ -2-2=-4 \\ -4=4 \\ \mathrm{This}\mathrm{is}\mathrm{true}. \end{gathered}$$

$$\begin{gathered} \mathrm{Also}\mathrm{substitute}x=-2, \\ y=-2\mathrm{into}\mathrm{the}\mathrm{equation} \\ -x+2y=-2 \\ -x+2y=-2 \\ -(-2)+2(-2)=-2 \\ 2-4=-2 \\ -2=-2 \\ \mathrm{This}\mathrm{is}\mathrm{true}. \end{gathered}$$

$$\begin{gathered} \mathrm{Also}\mathrm{substitute}x=-2, \\ y=-2\mathrm{into}\mathrm{the}\mathrm{equation} \\ -x+2y=-2 \\ -x+2y=-2 \\ -(-2)+2(-2)=-2 \\ 2-4=-2 \\ -2=-2 \\ \mathrm{This}\mathrm{is}\mathrm{true}. \end{gathered}$$