# Thread: Having trouble solving for a couple of variables

1. ## Having trouble solving for a couple of variables

It has been a while since I've had a math class and was having trouble solving for two variables. Here are the two equations I have:

a+b=w+x+y+z
ab=wy+wx+xz

I am trying to solve for a and b individually but am really having trouble. Am I missing something?

2. ## Re: Having trouble solving for a couple of variables

I was trying to solve this but hit a wall when I pluged equation 1 into 2. Here is what I did, maybe it will help you just a bit.

Spoiler:
If we are solving for $\displaystyle a$ and $\displaystyle b$, then they will be represented in terms of everything else. In this case $\displaystyle w,x,y,z$.

From equation 1:
$\displaystyle a+b=w+x+y+z \newline a=w+x+y+z-b$ or $\displaystyle b=w+x+y+z-a$
In any case just take the determined value of a or b from above and plug it into the second equation and isolate for the desired variable.

3. ## Re: Having trouble solving for a couple of variables

I also tried that and that's where I got stuck.

4. ## Re: Having trouble solving for a couple of variables

Originally Posted by thealbatross
It has been a while since I've had a math class and was having trouble solving for two variables. Here are the two equations I have:

a+b=w+x+y+z
ab=wy+wx+xz

I am trying to solve for a and b individually but am really having trouble. Am I missing something?
b = w + x + y + z - a means that a(w + x + y + z - a) = wx + wy + xz. Expanding it out gives

$\displaystyle -a^2 + (w + x + y + z)a = wx + wy + xz$

$\displaystyle a^2 - (w + x + y + z)a + (wx + wy + xz) = 0$

This is a quadratic equation in a and you can use the quadratic formula. It's going to be a terrible mess as I doubt it is going to give you any sort of "simple" answer.

-Dan