Question

Solve the system using any method (graphing, elimination, or substitution):
(1) 2x^2 + y^2 = 18
(2) xy = 4

I know I can't use elimination, and I don't know how I would graph the second one, so I'm trying substitution. Am I doing it right to far?

xy = 4
y = 4/x
then substitute into equation (1)
2x^2 + (4/x)^2 = 18
2x^2 + 16/(x^2) = 18

If I'm right, what's the next step? I'm a bit confused.

Answer 1

From where you stopped..
=>

\[2x^{2}+ 16/x^2 = 18\]
\[2x^4-18x^2+16 = 0\]
\[x^4-9x^2+8=0\]

Should be able to solve from there!

Answer 2

Thank you!