systems of nonlinear equations

Question

i need to help i have tried this problem but i cannot find the right answer i need to determine the real solutions for this:

x^2+4xy=10
4x^2-xy=6

Answer 1

multipy the bottom equation by 4
x^2+4xy=10
16x^2-4xy=24

add the equations

17x^2=34
solve for x, you get +-sqrt2

put each of those values into the first equation, and solve for y.
I will do the -sqrt2=x for you.

2-y4sqrt2=10
4ysqrt2=-8
y=-2/sqrt2= -sqrt2

now do the solution of y for x=+sqrt2