nonlinear system of equations problem

I can't figure out where I'm going wrong in solving this system of equations.

x^{2}+2xy-y^{2=}14

x^{2}-y^{2}= -16

Elimination

x^{2}+2xy-y^{2}=14

-x^{2}-0xy+y^{2}= 16

2xy=30

Substitution

x^{2}+30-y^{2}=14

x^{2}-y^{2}+30=14

-16+30=14

14=14

I keep getting results like this any way I try to substitute or rearrange the equations.

Re: nonlinear system of equations problem

Whenever you get an expression like 14=14 that means yuo have essentially made the same substitution twice, so you no longer have two independent equations.

Try this: note that x^2 + 2xy + y^2 = (x+y)^2, and that x^2-y^2 is the difference of two squares. So the two equations become:

Can you take it from here?

Re: nonlinear system of equations problem

The first equation was x^2+2xy-y^2=14 (not x^2 + 2xy + y^2 = 16)

I don't think x^2+2xy-y^2 can be factored any further. Can it?

Re: nonlinear system of equations problem

Re: nonlinear system of equations problem

Hello, cdbowman42!

Subtract [1] - [2]: .

Substitute into [2]: .

Multiply by

Factor: .

We have: .

Substitute into [3]: .

Therefore: .