Question

Which graph shows the solution to the following system?

Answer 1

we have

$y=\frac{1}{4} x-2$ -----> equation $1$

$y=\frac{7}{4} x+4$ -----> equation $2$

Resolve the system

we know that

the solution of the system is the intersection of both graphs

Multiply by $-1$ equation $1$

$-y=-\frac{1}{4} x+2$

Adds equation $1$ and equation $2$

$-y=-\frac{1}{4} x+2$

$y=\frac{7}{4} x+4\\ ------$

$0=\frac{6}{4}x +6\\ \\ 0=6x+24\\ 6x=-24\\ x=-4$

find the value of y

$y=\frac{7}{4}*(-4)+4\\ \\ y=-7+4\\ y=-3$

the solution is the point $(-4,-3)$

therefore

the answer is

The solution is the graph in the attached figure

Answer 2

Solve
y=1/4x-2
y=7/4x+4
since both equal y, set equalto each other
1/4x-2=7/4x+4
minus 1/4x from both sides
-2=6/4x+4
minus 4 from both sides
-6=6/4x
times 4 both sides
-24=6x
divide by 6
-4=x
sub back
y=1/4x-2
y=1/4(-4)-2
y=-1-2
y=-3
(-4,-3) is soluiton
starting at center go left 4 units and down 3 units
B is answer