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algebra intermediate

Problem

The value of

x

at the intersection of

y = \frac{8}{x ^{2} + 4}

and

x + y = 2

is:

(A)

- 2 + 5

(B)

- 2 - 5

(C)

0

(D)

2

Solution

x + y = 2 ⟹ y = 2 - x

. Then

2 - x = \frac{8}{x ^{2} + 4} ⟹ (2 - x) (x^{2} + 4) = 8

. We now notice that

x = 0 ⟹ (2) (4) = 8

, so

0

Final answer

C