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)