# Homework Help: Can anyone help me solve this equation system ?

1. Nov 15, 2008

### Dorotea

x³+y³=1
x²y+2xy²+y³=2

2. Nov 15, 2008

### gabbagabbahey

You could try solving the first equation for y and substituting it int the second....that will give you an equation in terms of x only.

3. Nov 15, 2008

### Staff: Mentor

Or you could solve for x in the 2nd equation, which is quadratic in x, by using the quadratic formula.
$$yx^2 + 2y^2 x + y^3 -2 = 0$$
You will of course get two equations for x.

4. Nov 17, 2008

### chaoseverlasting

You could expand (x+y)3 and then substitute the values for the two expressions that you have. That would be a lot simpler.

5. Nov 17, 2008

### Avodyne

Notice that both equations only have terms of degree 3 in both variables. So one thing you could do is let r=x/y, and divide both equations by y^3. Each left-hand side will then depend only on r, and each right-hand side only on y^3. Eliminating y^3 will give you a cubic equation in r. Solve this by guessing a root, or by graphing to get a root. Once you know one root you can reduce it to a quadratic to get the other two.