Question

Solve the following system of equations graphically on the set of axes below. y=-x-3 x-3y=-3

Answer 1

To draw any line on the plane, locate two points on it and cross them using a straight line.

Then, in our case, we need to find two points on each of the two lines

As for y= -x-3

`\begin{gathered} x=0 \\ \Rightarrow y=-0-3=-3 \\ \Rightarrow(0,-3) \\ x=1 \\ \Rightarrow y=-1-3=-4 \\ \Rightarrow(1,-4) \end{gathered}`

Similarly, in the case of x-3y=-3

`\begin{gathered} x=0 \\ \Rightarrow0-3y=-3 \\ \Rightarrow y=1 \\ \Rightarrow(0,1) \\ x=-3 \\ \Rightarrow-3-3y=-3 \\ \Rightarrow y=0 \\ \Rightarrow(-3,0) \end{gathered}`

Using the first set of points, graph y= -x-3, as shown below

Graphing the second line, x-3y=-3

Graph both lines at the same time and look for the intersection point

Then, the solution to the system of equations is (x,y)=(-3,0)