Question

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

$\left\{\begin{array}{l}x+y=6\\ x-y=-8\end{array}\right.$

Short answer

The solutions to the system of equations are$x=-1$and$y=7$.

Step-by-step solution

Step 1. Given information.

We have:

$\left\{\begin{array}{l}x+y=6\\ x-y=-8\end{array}\right.$

Step 2. Find the intercepts.      

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

The system of equations are:

$\left\{\begin{array}{l}x+y=6\\ x-y=-8\end{array}\right.$

x-intercept: substitute $y=0$

$$\begin{gathered} x+0=6 \\ x=6 \end{gathered}$$

X-intercept: $\left(6,0\right)$

$$\begin{gathered} x-0=-8 \\ x=-8 \end{gathered}$$

X-intercept: $\left(-8,0\right)$

y-intercept: substitute $x=0$

$$\begin{gathered} 0+y=6 \\ y=6 \end{gathered}$$

Y-intercept: $\left(0,6\right)$

$$\begin{gathered} 0-y=-8 \\ y=8 \end{gathered}$$

Y-intercept:role="math" localid="1647624842001" $\left(0,8\right)$

Step 3. Use the intercept to draw the graph.    

Graph the line and find the intersection point:

The lines intersect at $\left(-1,7\right)$.

Therefore, the solution are:

$x=-1,y=7$