Solving 2 equation with 2 variables (hard)

In summary, the conversation is about solving a problem involving equations with trigonometric components. The problem only allows for exact values to be found without using any programs. The conversation includes various strategies for finding a solution, such as rewriting the equations and using different methods for solving the equations. There is also a typo in the problem that must be corrected.
  • #1
Zetison
35
0
[PLAIN]http://folk.ntnu.no/jonvegar/images/math.gif [Broken]

I really need some help here (no program is allowed :smile:)
 
Last edited by a moderator:
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  • #2
What work have you done on the problem so far?
 
  • #3
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.
 
  • #4
The problem is to find exact values, not estimatet values. Therefore: do not use any programs...
 
  • #5
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.
 
  • #6
Here is what I have done so far:

[PLAIN]http://folk.ntnu.no/jonvegar/images/1.gif [Broken]
[PLAIN]http://folk.ntnu.no/jonvegar/images/2.gif [Broken]
[PLAIN]http://folk.ntnu.no/jonvegar/images/3.gif [Broken]
[PLAIN]http://folk.ntnu.no/jonvegar/images/4.gif [Broken]
[PLAIN]http://folk.ntnu.no/jonvegar/images/5.gif [Broken]
[PLAIN]http://folk.ntnu.no/jonvegar/images/6.gif [Broken]

But these solutions contains "cos". It is possible to rewrite the equations to the formula
[PLAIN]http://folk.ntnu.no/jonvegar/images/8.gif [Broken]
and then find solutions without any trigonometrical components.

That is my problem...
 
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  • #7
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?
 
  • #8
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.
 
  • #9
There is a typo in the problem: "79" should be "78".
 
  • #10
Is it just because the answer drops our nicely if that is the case, or do you somehow know it as a fact :S ?
 
  • #11
I just somehow know it is a fact :smile:
Count Iblis said:
There is a typo in the problem: "79" should be "78".
Sorry mac, it is "79"
 
Last edited:

1. How do I solve a system of two equations with two variables?

To solve a system of two equations with two variables, you can use the substitution method, elimination method, or graphing method. First, choose which method you prefer and solve one equation for one of the variables. Then, substitute this expression into the other equation and solve for the remaining variable. Finally, substitute the value of one variable into either equation to find the value of the other variable.

2. Can I use the substitution method for any system of two equations with two variables?

Yes, the substitution method can be used for any system of two equations with two variables. However, it may not always be the most efficient method. For example, if one of the equations is already solved for one of the variables, it may be easier to use the elimination method.

3. How do I know if a system of two equations with two variables has a solution?

A system of two equations with two variables will have a unique solution if the two lines intersect at one point. This means that the two lines are not parallel and have different slopes. If the two lines are parallel, they will never intersect and the system of equations will have no solution. If the two lines are the same, they will intersect at infinitely many points and the system of equations will have infinite solutions.

4. Can I solve a system of two equations with two variables graphically?

Yes, you can solve a system of two equations with two variables by graphing the two lines and finding the point of intersection. This method may be helpful if the equations are simple and easy to graph, but it may be less accurate than using algebraic methods.

5. What do I do if the system of equations I am trying to solve is inconsistent?

If a system of equations is inconsistent, it means that the equations do not have a common solution. This could happen if the two lines are parallel and never intersect, or if the two lines are the same. In this case, the system has no solution. You can check for inconsistency by solving the equations using any method and seeing if you get a contradiction, such as 0=1.

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