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1972 AHSME Problems/Problem 11

Revision as of 13:35, 4 February 2022 by Tylero 1.618 (talk | contribs) (→‎Solution)

Problem

The value(s) of $y$ for which the following pair of equations $x^2+y^2+16=0\text{ and }x^2-3y+12=0$ may have a real common solution, are

$\textbf{(A) }4\text{ only}\qquad \textbf{(B) }-7,~4\qquad \textbf{(C) }0,~4\qquad \textbf{(D) }\text{no }y\qquad \textbf{(E) }\text{all }y$

Solution

Because x2 + y2 + 16 = 0 has no real solutions, ∀ sets containing x2 + y2 + 16 = 0, no real solutions may exist.

– TylerO_1.618

∴ the solution is $\fbox{D}$

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