We can draw each line by assuming that x = 0 and y = 0 and solve each case.
In the first equation, we have the following:
[tex]\begin{gathered} x+y=-2 \\ x=0\Rightarrow y=-2 \\ y=0\Rightarrow x=-2 \end{gathered}[/tex]
notice that we have a pair of coordinate points (0,-2) and (-2,0). These two points will be useful when we draw the line.
Next, for the second equation we have:
[tex]\begin{gathered} 3x-y=-2 \\ x=0\Rightarrow-y=-2\Rightarrow y=2 \\ y=0\Rightarrow3x=-2\Rightarrow x=-\frac{2}{3} \end{gathered}[/tex]
in this case we have the points (0,2) and (-2/3,0). Now, if we draw both lines on the coordinate plane we get the following:
notice that both lines intersect on the point (-1,-1). Thus, the solution of the system of equations is the point (-1,-1)
