Question

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

$\left\{\begin{array}{l}x+y=-5\\ x-y=3\end{array}\right.$

Short answer

The solutions to the system of equations are$x=-1$and$y=-4$.

Step-by-step solution

Step 1. Given information.

We have:

$\left\{\begin{array}{l}x+y=-5\\ x-y=3\end{array}\right.$

Step 2. Find the intercepts.    

We will find thex-intercept andy-intercept of both equations and use them to graph the lines.

The system of equations are:

$\left\{\begin{array}{l}x+y=-5\\ x-y=3\end{array}\right.$

x-intercept: substitute $y=0$

$$\begin{gathered} x+0=-5 \\ x=-5 \end{gathered}$$

X-intercept: $\left(-5,0\right)$

$$\begin{gathered} x-0=3 \\ x=3 \end{gathered}$$

X-intercept:$\left(3,0\right)$

y-intercept: substitute $x=0$

$$\begin{gathered} 0+y=3 \\ y=3 \end{gathered}$$

Y-intercept:$\left(0,3\right)$

$$\begin{gathered} 0-y=3 \\ y=-3 \end{gathered}$$

Y-intercept:$\left(0,-3\right)$

Step 3. Use the intercept to draw the graph.  

Graph the line and find the intersection point:

The lines intersect are $\left(-1,-4\right)$.

Therefore, the solutions are:

$x=-1,y=-4$