Answer: Choice C
(2, 4) and (0, -4)
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Explanation:
Let's solve the first equation for y
4x - y = 4
-y = -4x+4
y = 4x-4
Now plug this into the other equation and solve for x.
2x^2 - y = 4
2x^2 - ( y ) = 4
2x^2 - ( 4x-4 ) = 4
2x^2 - 4x+4 = 4
2x^2 - 4x+4-4 = 0
2x^2 - 4x = 0
2x(x - 2) = 0
2x = 0 or x-2 = 0
x = 0 or x = 2
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If x = 0, then,
y = 4x-4
y = 4(0)-4
y = -4
This gives one solution as (0, -4)
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If x = 2, then,
y = 4x-4
y = 4(2)-4
y = 4
The other solution is (2, 4)
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To check the answers, plug the x and y coordinates into each equation. You should get the same thing on both sides.
Below is verification using a graph. The points of intersection are the solutions.
