we have
[tex] y=\frac{1}{4} x-2 [/tex] -----> equation [tex] 1 [/tex]
[tex] y=\frac{7}{4} x+4 [/tex] -----> equation [tex] 2 [/tex]
Resolve the system
we know that
the solution of the system is the intersection of both graphs
Multiply by [tex] -1 [/tex] equation [tex] 1 [/tex]
[tex] -y=-\frac{1}{4} x+2 [/tex]
Adds equation [tex] 1 [/tex] and equation [tex] 2 [/tex]
[tex] -y=-\frac{1}{4} x+2 [/tex]
[tex] y=\frac{7}{4} x+4\\ ------ [/tex]
[tex] 0=\frac{6}{4}x +6\\ \\ 0=6x+24\\ 6x=-24\\ x=-4 [/tex]
find the value of y
[tex] y=\frac{7}{4}*(-4)+4\\ \\ y=-7+4\\ y=-3 [/tex]
the solution is the point [tex] (-4,-3) [/tex]
therefore
the answer is
The solution is the graph in the attached figure
