Question

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

$\left\{\begin{array}{l}x+y=5\\ 2x-y=4\end{array}\right.$

Short answer

The solutions to the system of equations are$x=3$and$y=2$.

Step-by-step solution

Step 1. Given information.

We have:

$\left\{\begin{array}{l}x+y=5\\ 2x-y=4\end{array}\right.$

Step 2. Find the intercepts.   

We will find thex-intercept andy-intercept of both equations and use them to graph the lines.

The system of equations are:

$\left\{\begin{array}{l}x+y=5\\ 2x-y=4\end{array}\right.$

x-intercept: substitute $y=0$

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

X-intercept: role="math" localid="1647622844520" $\left(5,0\right)$

$$\begin{gathered} 2x-0=4 \\ x=2 \end{gathered}$$

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

y-intercept: substitute $x=0$

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

Y-intercept: $\left(0,5\right)$

$$\begin{gathered} 2\left(0\right)-y=4 \\ y=-4 \end{gathered}$$

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

Step 3. Use the intercept to draw the graph. 

Graph the line and find the intersection point:

The lines intersect at $\left(3,2\right)$.

Therefore, the solutions are:

$x=3,y=2$