Difference between revisions of "1972 AHSME Problems/Problem 11"
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==Problem== | ==Problem== | ||
| − | The value(s) of <math>y</math> for which the following pair of equations <math>x^2+y^2 | + | The value(s) of <math>y</math> for which the following pair of equations <math>x^2+y^2-16=0\text{ and }x^2-3y+12=0</math> may have a real common solution, are |
<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> | ||
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==Solution== | ==Solution== | ||
Revision as of 14:24, 28 June 2025
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
