Help solving a system of linear equations

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Discussion Overview

The discussion revolves around solving a system of linear equations to determine the percent abundance of two isotopes. Participants explore various methods for solving the equations, including substitution and Gaussian elimination.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant describes the system of equations and expresses difficulty in solving it using the addition/subtraction method.
  • Another participant suggests that the addition/subtraction method should work and mentions Gaussian elimination followed by back substitution as a valid approach.
  • A third participant requests to see the original poster's work to help identify any errors.
  • One participant humorously remarks on the nature of the forum, implying that the original poster's request for help may not align with the forum's expectations.
  • Another participant outlines a step-by-step method for solving the equations using substitution, detailing how to isolate variables and simplify the equations.
  • The original poster later acknowledges finding their mistake, indicating progress in their understanding.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best method to solve the equations, as multiple approaches are suggested. The discussion remains open with various viewpoints on solving the system.

Contextual Notes

Some participants may have different assumptions about the methods used, and there is no resolution of the original poster's specific error in the calculations.

Whitebread
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I haven't done this in a long time so please bare with me.

I need to solve this system to find the percent abundance of 2 isotopes.

68.9257x + 70.9249y=69.723
x+y=1

In order to solve the system by addition/subraction one would multiply 68.9257 through the second equation, then procede to subract right? I've been doing this, but I haven't been getting the right answer...

Help... :confused:
 
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...which should work. Then substitute the value of y you get into either equation. This method's called Gaussian Elimination followed by back substitution.
 
Well, if you show your work, maybe we can find your error.
 
"I haven't done this in a long time so please bare with me."

Hey, this isn't that kind of website!
 
The simplest way in this case is:
1. Rewrite your second equation as y=1-x
2. Substitute this expression for "y" into "y"'s place in the first equation
3. Collect the "x"'s on the left-hand side on your equation, and the "constants" at your right hand side.
4. Divide the resulting equation on both sides with the numerical factor appearing in front of your "x" symbol.
The resulting equation will look like:
x=some number.
5. Put "some number" into "x"'s place in the equation y=1-x to find the y-value
 
Thank you very much guys, I seem to have found my mistake.
 

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