# Simultaneous confusion

1. Feb 20, 2004

### Hypercase

how can the following pair of simultaneous eqns. be solved

a1X^m +b1Y^n =c1
a2X^m’+b2Y^n’=c2

2. Feb 20, 2004

### NateTG

What do you mean by m' ? Is it supposed to be the derivative of m?

3. Feb 20, 2004

### Hypercase

No by m' I mean that the exponent of X in the first equation is not the same as the second equation.
Here, Ive rewritten the equation:
a1X^m +b1Y^n =c1
a2X^p +b2Y^q =c2

4. Feb 20, 2004

### NateTG

So you have
$$a_1x^{n_1}+b_1y^{m_1}=c_1$$
and
$$a_2x^{n_2}+b_2y^{m_2}=c_2$$
Then
$$x=(\frac{c_2-b_2y^{m_2}}{a_2})^{\frac{1}{n_2}}$$
Then you can substitute to get:
$$a_1(\frac{c_2-b_2y^{m_2}}{a_2})^{\frac{n_1}{n_2}} + b_1y^{m_1}=c_1$$
which is an equation in a single variable. I'm not sure off the top of my head where to go from here, but that can definitely be solved numerically.

5. Feb 20, 2004

### Hypercase

I reached had reached so far, but I noticed that this is not an equation in one variable(duh!). But if the powers were really big it would become a hell of a job. Is there another way or a easier way to proceed from here.

6. Feb 20, 2004

### NateTG

Is there a particular problem that you're trying to solve?

7. Feb 20, 2004

### Hypercase

8. Feb 21, 2004

### NateTG

Ok, so what are the variables, and what is known?

9. Feb 21, 2004

### Hypercase

a1X^m +b1Y^n =c1
a2X^p +b2Y^q =c2

That is the eqn.
X,Y are the variables.