JEE Main Maths: Pair of Equations questions with solutions

Q1. Solve the system of equations: x² - y² = 16 and x + y = 8. Find (x, y).

1. x = 5, y = 3
2. x = 6, y = 2
3. x = 4, y = 4
4. x = 8, y = 0

Answer: x = 5, y = 3

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.