Question

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

$\left\{\begin{array}{l}x+y=4\\ x-y=0\end{array}\right.$

Short answer

The solutions to the system of equations are$x=2$and$y=2$.

Step-by-step solution

Step 1. Given information.

We have:

$\left\{\begin{array}{l}x+y=4\\ x-y=0\end{array}\right.$

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:

$\left\{\begin{array}{l}x+y=4\\ x-y=0\end{array}\right.$

x-intercept: substitute $y=0$

$$\begin{gathered} x+0=4 \\ x=4 \end{gathered}$$

X-intercept: $\left(4,0\right)$

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

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

y-intercept: substitute $x=0$

$$\begin{gathered} 0+y=4 \\ y=4 \end{gathered}$$

Y-intercept: $\left(0,4\right)$

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

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

Step 3. Use the intercept to draw the graph.   

Graph the line and find the intersection point:

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

Therefore, the solutions are:

$x=2,y=2$