To solve a system of equations graphically, we need to graph the equations. We need two points to graph a line. Substituting y = 0 into the equation of the first line, we get:
[tex]\begin{gathered} x=y-4 \\ x=0-4 \\ x=-4 \end{gathered}[/tex]Then, the line passes through the point (-4, 0). Substituting y = 4 into the equation of the first line, we get:
[tex]\begin{gathered} x=4-4 \\ x=0 \end{gathered}[/tex]Then, the line passes through the point (0, 4).
Now, considering the second line, substituting with y = 0 and y = 1, and solving for x, we get:
[tex]\begin{gathered} 2x=4y \\ 2x=4\cdot0 \\ 2x=0 \\ x=\frac{0}{2} \\ x=0 \end{gathered}[/tex][tex]\begin{gathered} 2x=4\cdot1 \\ x=\frac{4}{2} \\ x=2 \end{gathered}[/tex]Therefore, this line passes through the points (0, 0) and (2,1).
Connecting these points, each line is graphed as follows:
The solution to the system of equations is the point at which both lines intersect. From the graph, the solution is (-8, -4)
