Solve for x and y if x - y = 2 and x2 - y2 = 8
(-1, 3)
(3, 1)
(-3, 1)
(1, 3)
Correct answer is B
x - y = 2 ...........(1)
x2 - y2 = 8 ........... (2)
x - 2 = y ............ (3)
Put y = x -2 in (2)
x2 - (x - 2)2 = 8
x2 - (x2 - 4x + 4) = 8
x2 - x2 + 4x - 4 = 8
4x = 8 + 4 = 12
x = \(\frac{12}{4}\)
= 3
from (3), y = 3 - 2 = 1
therefore, x = 3, y = 1