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:

Figure5.1.9Graphs of \(y=\frac{1}{2}x+4\) and \(y=-x-5\text{.}\)

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