Nonlinear System Solution Strategies

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Homework Help Overview

The problem involves solving a nonlinear system of equations represented by \(x^2 - 2y^2 = 16\) and \(x^2 + y^2 = 25\). Participants are exploring methods to manipulate these equations to find solutions.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • The original poster attempts to solve the system by subtracting one equation from the other but expresses confusion about the steps and results. Some participants question the correctness of the original poster's manipulation of the equations, particularly regarding the treatment of the right-hand side (RHS) of the equations.

Discussion Status

The discussion includes attempts to clarify the process of subtraction in the equations, with some participants providing feedback on the original poster's calculations. There is an acknowledgment of confusion regarding the terms used, such as LHS and RHS, indicating a need for conceptual clarification.

Contextual Notes

Participants note the original poster's uncertainty about the steps to take after their initial manipulation, as well as the implications of arriving at negative values for \(y^2\), which raises questions about the validity of the solutions being pursued.

oray
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Homework Statement



Solve the nonlinear system.

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

Homework Equations



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?
 
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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 :)
 

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