Difference between revisions of "1972 AHSME Problems/Problem 11"
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<math>\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</math> | <math>\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</math> | ||
| + | ==Solution== | ||
| + | |||
| + | Because x<sup>2</sup> + y<sup>2</sup> + 16 = 0 has no real solutions, ∀ sets containing x<sup>2</sup> + y<sup>2</sup> + 16 = 0, no real solutions may exist. | ||
| + | |||
| + | ∴ the solution is <math>\fbox{D}</math> | ||
| + | |||
| + | |||
| + | – TylerO_1.618 | ||
Latest revision as of 13:37, 4 February 2022
Problem
The value(s) of 
for which the following pair of equations 
may have a real common solution, are
Solution
Because x2 + y2 + 16 = 0 has no real solutions, ∀ sets containing x2 + y2 + 16 = 0, no real solutions may exist.
∴ the solution is 
– TylerO_1.618
