Question

Solve the system of equations. 4x – y = 4 2x2 – y = 4 (0, 4) and (0, –4) (1, 0) and (1, –6) (2, 4) and (0, –4) (3, 8) and (0, –4)

Answer 1

Answer: Choice C

(2, 4) and (0, -4)

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Step-by-step 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.