solve this system by substitution?

y = -4x + 12 1/2
y = 1/4(x) + 4

y = -4x + 12 1/2
1/4(x) + 4 = -4x + 12 1/2
x/4 + 4 = -4x + 12 1/2
x/4 + 4x = -4 + 12 1/2
4(x/4 + 4x) = 4(17/2)
x + 16x = 34
17x = 34
x = 34/17
x = 2

y = -4x + 12 1/2
y = -4(2) + 12 1/2
y = -8 + 12 1/2
y = 4 1/2 (4.5)

∴ x = 2 , y = 4 1/2 (4.5)

-4x + 12.5 = 0.25x + 4

4.25x = 8.5
x = 2

sub this into one of the eqautions..

y = 4.5

:)

Question is unclear.
Do you mean:-
y = - 4x + 25/2
y = (1/4) x + 4

(1/4) x + 4 = - 4x + 25/2
x + 16 = - 16x + 50
17x = 34
x = 2

y = - 8 + 25/2
y = - 16/2 + 25/*2
y = 9/2

x = 2 , y = 9/2

I'm going to call the first equation (1) and th4 second (2)

Subtract (2) from (1)

0 = -(4 1/4)x + 8 1/2 Multiply both sides of the equation by 4 to get rid if the fractions. Note: 4 1/4 = 17/4 and 8 1/2 = 17/2

0 = -17x + 34

17x = 34
x = 2

Substituting 2 for x in equation (2) y = 1/2 +4 = 9/2

So your final answer is x = 2, y = 9/2. <<<<<
I have checked the answers and they are correct.