To solve the system of equations graphically, plot both lines and find the coordinates of the intersection point.
To plot a line, evaluate the equation for two different values of x to find the corresponding values of y. Plot the points that were found by doing so, and draw a line between them.
Take for instance the values x=0 and x=5. For the first equation:
[tex]\begin{gathered} y=x+4 \\ x=0\Rightarrow y=0+4\Rightarrow y=4 \\ x=5\Rightarrow y=5+4\Rightarrow y=9 \end{gathered}[/tex]
Then, the points (0,4) and (5,9) lie on that line:
Repeat the procedure for the equation y=-x+8. By doing so, we find the points (0,8) and (5,3):
We can see that the lines intersect at the point (2,6).
Therefore, the solution to this system is:
[tex]\begin{gathered} x=2 \\ y=6 \end{gathered}[/tex]
