Question

How many solutions dose this liner system have ? y=2x-5 -8x4y=-20

Answer 1

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).