What is y=-6x=7
y=8x-21 in solving system by substitution method?

So,

Notice that y is equal to two different equations.

Since we know that, we can simply put the right sides of both equations side-by-side.

-6x + 7 = 8x - 21

Add 6x to both sides
7 = 14x - 21

Add 21 to both sides
28 = 14x

Divide both sides by 14
2 = x

Substitute in the second equation
y = 8(2) - 21

Distribute
y = 16 - 21

Collect Like Terms
y = -5

Check
-5 = -6(2) + 7
-5 = -12 + 7
-5 = -5 This checks.

Check in second equation
-5 = 8(2) - 21
-5 = 16 - 21
-5 = -5 This also checks.

S = {(2,-5)}