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
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
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)
Source: Myschool Past Questions Archive (Record #31901)