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1972 AHSME Problems/Problem 11

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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 (Rigorous)

Solution (Quick)

Checking the answer choices, we see that only 4 is the viable choice. Therefore, the answer is $\boxed{A}$

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