1988 AHSME Problems/Problem 17
Problem
If and , find
Solution
We proceed by casework:
Case 1: x, y >= 0
Thus we have 2x + y = 10, x = 12. This makes y < 0, a contradiction.
Case 2: x >= 0 > y
2x + y = 10, x - 2y = 12. By multiplying the first equation by two and adding, we have 4x + x = 2*10 + 12 thus x = 32/5. Since the question only specifies 1 solution, plugging in x = 32/5 into the first equation yields y = -14/5 thus x + y = 18/5 .
See also
1988 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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