Question

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

$\left\{\begin{array}{l}-x+y=-3\\ 4x+4y=4\end{array}\right.$

Short answer

The solutions to the system of equations are:

$x=2,y=-1$

Step-by-step solution

Step 1. Given information.

We have:

$\left\{\begin{array}{l}-x+y=-3\\ 4x+4y=4\end{array}\right.$

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:

$\left\{\begin{array}{l}-x+y=-3\\ 4x+4y=4\end{array}\right.$

x-intercept: substitute $y=0:$

localid="1647600186256" $$\begin{gathered} -x+0=-3 \\ x=3 \end{gathered}$$

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

role="math" localid="1647600263553" $$\begin{gathered} 4x+4\left(0\right)=4 \\ 4x=4 \\ x=1 \end{gathered}$$

X-intercept:$\left(1,0\right)$

y-intercept: substitute $x=0:$

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

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

$$\begin{gathered} 4\left(0\right)+4y=4 \\ 4y=4 \\ y=1 \end{gathered}$$

Y-intercept:$\left(0,1\right)$

Step 3. Use the intercept to draw the graph.

Graph the line and find the intersection point:

The lines intersect at $\left(2,-1\right)$.

Therefore, the solutions are:

$x=2,y=-1$