Question

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

$\left\{\begin{array}{l}-3x+y=-1\\ 2x+y=4\end{array}\right.$

Short answer

The solutions to the system of equations are$x=1,x=2$.

Step-by-step solution

Step 1. Given information.

We have:

$\left\{\begin{array}{l}-3x+y=-1\\ 2x+y=4\end{array}\right.$

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:

$\left\{\begin{array}{l}-3x+y=-1\\ 2x+y=4\end{array}\right.$

x-intercept: substitute $y=0$

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

X-intercept: $\left(\frac{1}{3},0\right)$

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

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

y-intercept: substitute $x=0$

$$\begin{gathered} -3\left(0\right)+y=-1 \\ y=-1 \end{gathered}$$

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

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

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 $(1,2)$.

Therefore, the solutions are:

$x=1,x=2$