# System involving nonlinear equations.

What is the best approach for obtaining the inverse of a system of equations involving nonlinear equations?
Say:
3x^2 - 2y = i
x + y = j
Solving for x and y in terms of i and j?
Note: This is not a homework problem, just a general question.

## Answers and Replies

Char. Limit
Gold Member
What is the best approach for obtaining the inverse of a system of equations involving nonlinear equations?
Say:
3x^2 - 2y = i
x + y = j
Solving for x and y in terms of i and j?
Note: This is not a homework problem, just a general question.
Here, I would say y=j-x then substitute that in for y.

3x^2 - 2(j-x) = i

Solve for x...

$$x = \pm \frac{1}{3} \left(\sqrt{6 j+3 i+1}-1\right)$$

Then, knowing what x is, substitute x in the second equation to express y in terms of i and j.

Here, I would say y=j-x then substitute that in for y.

3x^2 - 2(j-x) = i

Solve for x...

$$x = \pm \frac{1}{3} \left(\sqrt{6 j+3 i+1}-1\right)$$

Then, knowing what x is, substitute x in the second equation to express y in terms of i and j.
Thanks a lot. For some reason, I have always had difficulty with simple things like these!

There are no workable non lin equations that aren't reduced to a sum lin eqautions

blah blah blah

The real sht is identifying lin equations to reality