###### Example5.1.8

Solve the following system of equations by graphing:

\begin{equation*}
\left\{
\begin{alignedat}{4}
y \amp {}={} \amp \frac{1}{2}x \amp {}+{} \amp 4 \\
y \amp {}={} \amp {-x} \amp {}-{} \amp 5 \\
\end{alignedat}
\right.
\end{equation*}

Notice that each of these equations is written in slope-intercept form. The first equation, \(y=\frac{1}{2}x+4\text{,}\) is a linear equation with a slope of \(\frac{1}{2}\) and a \(y\)-intercept of \((0,4)\text{.}\) The second equation, \(y=-x-5\text{,}\) is a linear equation with a slope of \(-1\) and a \(y\)-intercept of \((0,-5)\text{.}\) We'll use this information to graph both lines:

The two lines intersect where \(x=-6\) and \(y=1\text{,}\) so the solution of the system of equations is the point \((-6,1)\text{.}\) We write the solution set as \(\{(-6,1)\}\text{.}\)