Question

What are the number of solutions to the system x2 - 2y2 = 12 and 2x2 + y2 = 4?
(NOTE: JUST THE NUMBER OF SOLUTIONS.)

Answer 1

if we multiply second equation by 2 we get
4x^2+ 2y^2 = 8

adding this to equation 1 gives us an equation in x only which we can solve for x

so what do you think ?

Answer 2

1 Solution only?

Answer 3

Oh ok, Im thinking no solutions

Answer 4

hmm let me think a bit more about this one..

Answer 5

we get 5x^2 = 20
x = +2 , -2

Answer 6

plugging 2 or -2 into equation 1 gives

4 - 2y2 = 12
2y^2 = -8
y^2 = -1
- no real values of y

so there is no real value of y corresponding to 2 or -2

yes you are right - no real solution

Answer 7

Thank You!

Answer 8

yw