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Solve the system of equations: x² - y² = 16 and x + y = 8. Find (x, y).
- x = 5, y = 3
- x = 6, y = 2
- x = 4, y = 4
- x = 8, y = 0
Correct answer: x = 5, y = 3
Solution
x² - y² = (x+y)(x-y) = 16. Since x + y = 8, 8(x - y) = 16 => x - y = 2. Solving x + y = 8 and x - y = 2: 2x = 10 => x = 5, y = 3.
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