Solve a system of linear equations by graphing.

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

The given linear system of equations is as follows:

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

The standard form of slope-intercept form is given by $y=mx+b$, where $m$denotes the slope and $b$denotes the $y$-intercept.

Assume the first equation $-3x+y=-1$.

$y=3x-1$

So, the slope localid="1647605936862" $m$is $3$and the $y$-intercept $b$is $-1$.

Assume the second equation$2x+y=4$.

$y=-2x+4$

So, the slope $m$is $-2$and the $y$-intercept $b$is $4$.

The graph of the two given lines is shown below:

From the graph, observe that the point of intersection is $(1,2)$.

Substitute the values of the variables into each equation to check whether a point is a solution to a given system of two equations.

If the point makes both equations true, it is a solution to the given system.

Substitute$1$for $x$and localid="1647606176390" $2$for $y$into localid="1647605719215" $-3x+y=-1$.

localid="1647606218465" $\begin{array}{rcl}-3\left(1\right)+2& =& -1\\ -3+2& =& -1\\ -1& =& -1\left(\text{True}\right)\end{array}$

Substitute localid="1647606168232" $1$for $x$and localid="1647606183746" $2$for $y$intolocalid="1647605751261" $\begin{array}{rcl}2x+y& =& 4\end{array}$.

localid="1647606251326" $\begin{array}{rcl}2\left(1\right)+2& =& 4\\ 2+2& =& 4\\ 4& =& 4\text{True}\end{array}$

Conclude that the point localid="1647606136185" $(1,2)$made both equations true.

Hence, localid="1647606142597" $(1,2)$is a solution.