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)}