Question

Which graph shows the solution to the following system?

Answer 1

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

Answer 2

we have

`y=(1)/(4) x-2` -----> equation
`1`

`y=(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=-(1)/(4) x+2`

Adds equation
`1` and equation
`2`

`-y=-(1)/(4) x+2`

`y=(7)/(4) x+4\\ ------`

`0=(6)/(4)x +6\\ \\ 0=6x+24\\ 6x=-24\\ x=-4`

find the value of y

`y=(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