# Help solving a system of linear equations

1. Aug 26, 2004

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............

2. Aug 27, 2004

### speeding electron

...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. Aug 27, 2004

### Hurkyl

Staff Emeritus
Well, if you show your work, maybe we can find your error.

4. Aug 27, 2004

### HallsofIvy

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

Hey, this isn't that kind of website!

5. Aug 27, 2004

### arildno

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. Aug 28, 2004