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Find the values of y which satisfy the simultaneous equations x + y = 5,…

Find the values of y which satisfy the simultaneous equations x + y = 5, x2 – 2y2 = 1
  • A.
    -12, -2
  • B.
    -12, 12
  • C.
    12, -2
  • D.
    2, -2
Correct Answer: Option C
Explanation

x + y = 5…….(i)
x2 – 2y2 = 1…….(ii)
x = 5 – y………(iii)
Subst. for x in eqn.(ii) = (5 – y)2 – 2y2 = 1
25- 10y + y2 – 2y2 = 1
25 – 1 = y2 + 10y
y2 + 10y2 – 24 = 0
(y + 12)(y – 2) = 0
Then Either y + 12 = 0 or y – 2 = 0
= (12, -2)