Solve each system by graphing:

$$\begin{gathered} x-3y=-3 \\ x+y=5 \end{gathered}$$

The system of equations are

$$\begin{gathered} x-3y=-3 \\ x+y=5 \end{gathered}$$

First equation:

$x-3y=-3$

Find x-intercept

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

role="math" localid="1647617178939" $$\begin{gathered} x-3\times 0=-3 \\ x-0=-3 \\ x=-3 \end{gathered}$$

So, x-intercept is $(-3,0)$

Find y-intercept

Plug $x=0$and find$y$value

$$\begin{gathered} 0-3y=-3 \\ -3y=-3 \\ \frac{-3y}{-3}=\frac{-3}{-3} \\ y=1 \end{gathered}$$

So, y-intercept is$(0,1)$

Second equation:

$x+y=5$

Find x-intercept

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

So, x-intercept is $(5,0)$

Find y-intercept

$$\begin{gathered} 0+y=5 \\ y=5 \end{gathered}$$

So, y-intercept is$(0,5)$

First equation:

Locate points$(-3,0),(0,1)$ and join them to get the line.

Second equation:

Locate points$(5,0),(0,5)$ on the graph and join them to get the line.

If the lines intersect, identify the point of intersection.

If lines are parallel, the system has no solution.

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

The graph is

Here, the intersection point is $(3,2)$

So, the solution is$(3,2)$