# Nonlinear System Solution Strategies

• oray
In summary, the problem is to solve the nonlinear system of equations x^2-2y^2=16 and x^2+y^2=25. The attempt at a solution involved subtracting one equation from the other, but the right-hand side was not subtracted correctly. The correct solution is y=null.
oray

## Homework Statement

Solve the nonlinear system.

x^2-2y^2=16
x^2+y^2=25

n/a?

## The Attempt at a Solution

ive tried subtracting 1 equation from the other...
(x^2-2y^2+9)=25
-(x^2+y^2)=25
-3y^2+9=25
-3y^2=16
y^2=-16/3
y=root of -16/3...
im not even sure if that part is right, also, i don't know where to go after that.
help?

You've forgotten to subtract the RHS as well.

huh? I am confused? what is the RHS? i really am confused on where to start in general.

Last edited:
oray said:
huh? I am confused? what is the RHS? i really am confused on where to start in general.

When you subtracted one equation from the other, you subtracted the left-hand side (LHS) of your equations, but did not do the same for the right-hand side (RHS), which was 25-25 = 0.

okay...
(x^2-2y^2+9)=25
-(x^2+y^2)=25
-3y^2+9=0
-3y^2=-9
y^2=-3
y=null?

You have -3y^2=(-9). That doesn't give you y^2=(-3), does it? I think I remember once dividing -9 by -3 and I didn't get -3.

awesome. figured it out. thanks for all the help people :)

## 1. What is a nonlinear system?

A nonlinear system is a mathematical model or set of equations that does not have a linear relationship between the input and output variables. This means that the output cannot be predicted by simply scaling the input. Nonlinear systems can have complex relationships and often require more advanced techniques to solve.

## 2. Why is solving nonlinear systems important?

Solving nonlinear systems is important because many real-world problems cannot be accurately modeled using linear equations. Nonlinear systems allow for more complex and accurate representations of natural phenomena, making them crucial in fields such as physics, engineering, and economics.

## 3. What methods are used to solve nonlinear systems?

There are several methods that can be used to solve nonlinear systems, including substitution, elimination, graphing, and iterative methods such as Newton's method and the bisection method. Additionally, computer software and calculators can be used to solve nonlinear systems numerically.

## 4. What are some challenges of solving nonlinear systems?

Solving nonlinear systems can be challenging because they often involve complex equations that cannot be solved algebraically. This means that numerical methods must be used, which can be time-consuming and may require multiple iterations to reach a solution. Additionally, nonlinear systems can have multiple solutions or no solutions at all, making them difficult to solve.

## 5. How do you know if a solution to a nonlinear system is valid?

A solution to a nonlinear system is valid if it satisfies all of the equations in the system. This can be checked by plugging the values into each equation and ensuring that the resulting equations are true. Additionally, a solution should also make sense in the context of the real-world problem being modeled.

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