# System of equations with 2 parameters

1. Jun 2, 2013

### Hivoyer

1. The problem statement, all variables and given/known data
I have a system of two equations:

3*x^2 - x + 3*y^2 = 0
2*x^2 - y + 2*y^2 = 0

2. Relevant equations

3. The attempt at a solution
I don't know how to express one with the other.I mean I can either have x = 3*y^2 + 3*x^2 or y = y = -2*y^2 - 2*x^2 and in both cases it becomes an utter mess.What can I do?

2. Jun 2, 2013

### Staff: Mentor

I would modify the second equation to get x^2 = ... and therefore x = ... and use this in the first equation.

3. Jun 2, 2013

### LCKurtz

Here's another suggestion. You can see by inspection that (0,0) is one intersection point. Since both equations represent circles, put them in standard form and locate their centers. Determine the slope $m_1$ of the line of centers. The slope of the common chord between their intersection points will be $m_2=-\frac 1 {m_1}$. The line through the origin with that slope $m_2$ whose equation is $y=m_2x$ will pass through the other intersection point. Solve that with one of your circles. It works out pretty easily.

4. Jun 3, 2013

### haruspex

One more suggestion: can you spot a multiplier that makes the quadratic terms in one equation the same as those in the other?

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