# Solving 2 equation with 2 variables (hard)

by Zetison
Tags: equation, solving, variables
 P: 35 I really need some help here (no program is allowed )
 PF Patron P: 7,122 What work have you done on the problem so far?
 PF Patron Sci Advisor Thanks Emeritus P: 38,395 I'm not sure why you would consider that "hard". You can solve the second equation for x as a quadratic function of y. Putting that into the first equation gives a cubic equation for y.
P: 35

## Solving 2 equation with 2 variables (hard)

The problem is to find exact values, not estimatet values. Therefore: do not use any programs...
 HW Helper P: 3,353 Indeed. Do you have any strategies to find a root? There are many you can try. Once you find one, you can divide and just solve a quadratic.
 P: 35 Here is what I have done so far: But these solutions contains "cos". It is possible to rewrite the equations to the formula and then find solutions without any trigonometrical components. That is my problem...
 HW Helper P: 3,353 Would have been a simpler computation for the program to have changed the x into 1/y rather than the other way around, small numbers to deal with overall. Were you expected to solve this cubic analytically and it's roots actually looked like that?
 P: 35 Yes. It does not matter how you start. You will get the same solutions with the same trigonometrical components. Plz help me find solutions without any trigonometrical components.
 P: 2,141 There is a typo in the problem: "79" should be "78".
 HW Helper P: 3,353 Is it just because the answer drops our nicely if that is the case, or do you somehow know it as a fact :S ?
P: 35
I just somehow know it is a fact
 Quote by Count Iblis There is a typo in the problem: "79" should be "78".
Sorry mac, it is "79"

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