The answer would be infinitely many solutions if your system is y = 2x - 5, -8x + 4y = -20. The answer would be (5/2, 0) if your system is y = 2x - 5, -8x - 4y = -20.
y = 2x - 5
-8x + 4y = -20
-8x + 4(2x - 5) = -20
-8x + 8x - 20 = -20
-20 = -20
True, so this system has infinitely many solutions.
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y = 2x - 5
-8x = 4y = -20
-8x - 4(2x - 5) = -20 -8(2.5) - 4y = -20
-8x - 8x + 20 = -20 -20 - 4y = -20
-16x + 20 = -20 + 20 + 20
- 20 - 20 ------------------------
-------------------------- -4y = 0
-16x = -40 ------ ----
-------- -------- 4 4
-16 -16
y = 0
x = 2.5
The final solution for this system is (2.5, 0) or (5/2, 0).