Find the values of y which satisfy the simultaneous equations x + y = 5, x2 - 2y2 = 1
-12, -2
-12, 12
-12, +2
2, -2
Correct answer is C
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)