South African Mathematics Olympiad

Question

If 2x + 2y = 14 and x^2 - y^2 = 21 then x - y is equal to (A) 1 (B) 2 (C) 3 (D) 4 (E) -1

Accepted Answer

Since 2x + 2y = 14, we have x + y = 7. Also since x^2 - y^2 = (x + y)(x - y), we have 7(x - y) = 21, so x - y = 21/7 = 3.