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 (Rigorous) == | |
| − | |||
| − | + | ==Solution (Quick)== | |
| + | Checking the answer choices, we see that only 4 is the viable choice. Therefore, the answer is <math>\boxed{A}</math> | ||
Latest revision as of 14:27, 28 June 2025
Problem
The value(s) of 
for which the following pair of equations 
may have a real common solution, are
Solution (Rigorous)
Solution (Quick)
Checking the answer choices, we see that only 4 is the viable choice. Therefore, the answer is 
