Solve for x and y if x - y = 2 and x\(^2\) - y\(^2\) = 8
A
(-1, 3)
B
(3, 1)
C
(-3, 1)
D
(1, 3)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
x - y = 2 ...........(1)
x\(^2\) - y\(^2\) = 8 ........... (2)
x - 2 = y ............ (3)
Put y = x - 2 in (2)
x\(^2\) - (x - 2)\(^2\) = 8
x\(^2\) - (x\(^2\) - 4x + 4) = 8
x\(^2\) - x\(^2\) + 4x - 4 = 8
4x = 8 + 4 = 12
x = \(\frac{12}{4}\)
= 3
from (3), y = 3 - 2 = 1
therefore, x = 3, y = 1
Source: Myschool Past Questions Archive (Record #29568)