X + y = - 2 \\ 3x - y = - 2draw each line and estimate the solution.

Question

`x + y = - 2 \\ 3x - y = - 2`draw each line and estimate the solution.

Answer 1

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:

`\begin{gathered} x+y=-2 \\ x=0\Rightarrow y=-2 \\ y=0\Rightarrow x=-2 \end{gathered}`

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:

`\begin{gathered} 3x-y=-2 \\ x=0\Rightarrow-y=-2\Rightarrow y=2 \\ y=0\Rightarrow3x=-2\Rightarrow x=-(2)/(3) \end{gathered}`

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)