Solve Systems of Equations by Graphing: example 5.4

We’ll solve both of these equations for $y$ so that we can easily graph them using their slopes and y-intercepts. $\{\begin{array}{c}3x+y=\mathrm{-1}\hfill \\ 2x+y=0\hfill \end{array}$

Solve the first equation for y. Find the slope and y-intercept. Solve the second equation for y. Find the slope and y-intercept.	$\begin{array}{c}\begin{array}{ccc}\hfill 3x+y& =\hfill & -1\hfill \\ \hfill y& =\hfill & -3x-1\hfill \\ \\ \hfill m& =\hfill & -3\hfill \\ \hfill b& =\hfill & -1\hfill \\ \\ \\ \hfill 2x+y& =\hfill & 0\hfill \\ \hfill y& =\hfill & -2x\hfill \\ \\ \hfill m& =\hfill & -2\hfill \\ \hfill b& =\hfill & 0\hfill \\ \hfill \end{array}\end{array}$
Graph the lines.
Determine the point of intersection.	The lines intersect at (−1, 2).
Check the solution in both equations.	$\begin{array}{cccc}\begin{array}{ccc}\hfill 3x+y& =\hfill & -1\hfill \\ \hfill 3(-1)+2& \stackrel{?}{=}\hfill & -1\hfill \\ \hfill -1& =\hfill & -1✓\hfill \end{array}& & & \begin{array}{ccc}\hfill 2x+y& =\hfill & 0\hfill \\ \hfill 2(-1)+2& \stackrel{?}{=}\hfill & 0\hfill \\ \hfill 0& =\hfill & 0✓\hfill \end{array}\end{array}$
	The solution is (−1, 2).