Help solving a system of linear equations

In summary, the conversation involves solving a system to find the percent abundance of 2 isotopes. The method discussed is Gaussian Elimination followed by back substitution, but a simpler method is suggested and explained. The conversation ends with one of the participants thanking the others for their help.
  • #1
Whitebread
23
0
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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  • #2
...which should work. Then substitute the value of y you get into either equation. This method's called Gaussian Elimination followed by back substitution.
 
  • #3
Well, if you show your work, maybe we can find your error.
 
  • #4
"I haven't done this in a long time so please bare with me."

Hey, this isn't that kind of website!
 
  • #5
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
 
  • #6
Thank you very much guys, I seem to have found my mistake.
 

1. What is a system of linear equations?

A system of linear equations is a set of equations that involve two or more variables and can be solved simultaneously to find the values of those variables that satisfy all the equations.

2. How do I solve a system of linear equations?

To solve a system of linear equations, you can use various methods such as substitution, elimination, or graphing. These methods involve manipulating the equations to isolate one variable and then substituting it into the other equations to solve for the remaining variables.

3. Can a system of linear equations have more than one solution?

Yes, a system of linear equations can have one, infinite, or no solutions. If the equations are independent, they will have a unique solution. If they are dependent, they will have infinite solutions. And if they are inconsistent, they will have no solutions.

4. What is the importance of solving a system of linear equations?

Solving a system of linear equations is important in various fields such as engineering, economics, physics, and many others. It helps in finding the intersection points of two or more lines, which can be used to make predictions, make decisions, or solve real-world problems.

5. Can I use a calculator to solve a system of linear equations?

Yes, you can use a calculator to solve a system of linear equations. Most scientific and graphing calculators have built-in functions that can solve systems of equations using different methods. However, it is important to understand the concepts and methods behind the calculations to ensure accuracy and to better understand the solution.

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