Solve each system by graphing:

$$\begin{gathered} x+y=2 \\ x-y=-8 \end{gathered}$$

The system of equations is

$$\begin{gathered} x+y=2 \\ x-y=-8 \end{gathered}$$

The first equation is

$x+y=2$

x-intercept:

Plug $y=0$and solve for $x$

$$\begin{gathered} x+0=2 \\ x=2 \end{gathered}$$

So, the x-intercept is $(2,0)$

y-intercept:

Plug $x=0$and find $y$

$$\begin{gathered} 0+y=2 \\ y=2 \end{gathered}$$

So, the y-intercept is$(0,2)$

Second equation is

$x-y=-8$

x-intercept:

Plug $y=0$and solve for $x$

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

So, the x-intercept is $(-8,0)$

y-intercept:

Plug $x=0$and find $y$

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

So, the y-intercept is$(0,8)$

First equation:

Locate points$(2,0),(0,2)$ on the graph and then join them to get the graph

Second equation:

Locate points$(-8,0),(0,8)$ on the graph and then join them to get the graph

So, the graph is

If the lines intersect, identify the point of intersection.

If lines are parallel, the system has no solution.

If lines are the same, the system has an infinite number of solutions.

The graph is

Here, the intersection point is$(-3,5)$