Solving Nonlinear System: 3x2+2y2=35, 4x2-3y2=24

In summary, the conversation involves solving a system of equations involving x and y. The original attempt at a solution involved rearranging for y^2 but resulted in incorrect answers. Another person suggests multiplying the equations and adding them. The original poster still has a question about why their original approach did not work, and it is discovered that there was a basic arithmetic error in their rearrangement of the equations.
  • #1
Stratosphere
373
0

Homework Statement


solve the system of [tex]3x^{2}+2y^{2}=35[/tex] and
[tex]4x^{2}-3y^{2}=24[/tex]


Homework Equations





The Attempt at a Solution


I re arranged for y^2 and got [tex]1\frac{1}{3}x^{2}-16=y^{2}[/tex] I keep getting x to equal \pm 2.473 this is clearly wrong, the answers should be (–3, –2), (–3, 2), (3, –2), and (3, 2). What am I doing wrong?
 
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  • #2
Instead of messing with fractions, why not just multiply the first equation by 3, the second equation by 2 and then just add them?
 
  • #3
rock.freak667 said:
Instead of messing with fractions, why not just multiply the first equation by 3, the second equation by 2 and then just add them?

Thanks for the help but I still have a question, after I combined the two equations how come it worked and it didn’t work when I rearranged them. Did I mess up?
 
  • #4
Looks like a basic arithmetic error. Because of the "[itex]1\frac{1}{3}[/itex]", which would better be left 4/3, it looks like you solved the second equation for y2: [itex]3y^2= 4x^2- 24[/itex] so [itex]y^2= (4/3)x^2- 8[/itex]. 24/3= 8, not 16.
 

1. How do you solve a nonlinear system?

To solve a nonlinear system, you can use various methods such as substitution, elimination, or graphical methods. These methods involve manipulating the equations to isolate one variable and solve for its value, then using that value to solve for the other variable.

2. What is a nonlinear system of equations?

A nonlinear system of equations is a set of equations where at least one of the equations contains variables raised to a power other than 1. This means that the relationship between the variables is not a straight line, making it more complex to solve compared to linear systems.

3. Can a nonlinear system have more than two equations?

Yes, a nonlinear system can have any number of equations. However, the more equations there are, the more difficult it can be to solve the system, especially if it does not have a unique solution.

4. What are the common methods for solving a nonlinear system?

The most common methods for solving a nonlinear system are substitution, elimination, and graphical methods. Other methods include using matrices and advanced numerical methods such as Newton's method or the Bisection method.

5. How do you check if a solution is correct for a nonlinear system?

To check if a solution is correct, you can substitute the values of the variables into each equation and see if they satisfy the equations. The solution should make all the equations true, otherwise, it is not a valid solution for the nonlinear system.

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