###### 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 $$\{(-6,1)\}\text{.}$$

in-context