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

^{2}– 2y^{2}= 1-
**A.**

-12, -2 -
**B.**

-12, 12 -
**C.**

12, -2 -
**D.**

2, -2

##### Correct Answer: Option C

##### Explanation

x + y = 5…….(i)

x^{2} – 2y^{2} = 1…….(ii)

x = 5 – y………(iii)

Subst. for x in eqn.(ii) = (5 – y)^{2} – 2y^{2} = 1

25- 10y + y^{2} – 2y^{2} = 1

25 – 1 = y^{2} + 10y

y^{2} + 10y^{2} – 24 = 0

(y + 12)(y – 2) = 0

Then Either y + 12 = 0 or y – 2 = 0

= (12, -2)