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Solve for x and y if x – y = 2 and x2 – y2…

Solve for x and y if x – y = 2 and x2 – y2 = 8
  • A.
    (-1, 3)
  • B.
    (3, 1)
  • C.
    (-3, 1)
  • D.
    (1, 3)
Correct Answer: Option B
Explanation

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