Question

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

$\left\{\begin{array}{l}x-y=2\\ 2x-y=6\end{array}\right.$

Short answer

The solutions to the system of equations are$x=4$and$y=2$.

Step-by-step solution

Step 1. Given information.

We have:

$\left\{\begin{array}{l}x-y=2\\ 2x-y=6\end{array}\right.$

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:

$\left\{\begin{array}{l}x-y=2\\ 2x-y=6\end{array}\right.$

x-intercept: substitute role="math" localid="1647623519744" $y=0$

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

X-intercept: $\left(2,0\right)$

$$\begin{gathered} 2x-0=6 \\ x=3 \end{gathered}$$

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

y-intercept: substitute $x=0$

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

Y-intercept: $\left(0,-2\right)$

$$\begin{gathered} 2\left(0\right)-y=6 \\ y=-6 \end{gathered}$$

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

Step 3. Use the intercept to draw the graph.  

Graph the line and find the intersection point:

The lines intersect at $\left(4,2\right)$.

Therefore, the solutions are:

$x=4,y=2$