# Struggling to solve a certain system of equations with unknown coefficients

$2 = A_0 + A_1$

$0 = -A_0 + X_1A_1$

$2/3 = A_0 + X_1^2A_1$

I'm trying to find values for $A_0, A_1$, and $X_1$. If I knew $X_1$ this would be a pretty simple process (I'd probably just plug it into a matrix or set $A_0 = 2 - A_1$ and solve), but with that being an unknown I'm sort of confused as to how I should be going about this.

Any help would be appreciated!

I also don't know what tag to give this. I was looking for one for System of Equations but there doesn't seem to be one. I assumed Matrices would be an appropriate tag since I'd guess you could solve this with a matrix.

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$X_1$ is an unknown. You have three equations in three unknowns-is the problem that it appears squared? The substitution method still works, though sometimes it increases the degree and sometimes it gets you roots you don't like. mythealias takes you through this one nicely, my comment hopes to have you not scared of these in the future. – Ross Millikan Nov 11 '12 at 3:59

Add first two equations to get $$2 = A_1(1 + X_1)$$ Add last two equations to get $$2/3 = A_1 X_1 (1 + X_1)$$ From this it follows, $X_1 = 1/3$. substitute back to get $A_1 = 3/2$ and $A_0 = 1/2$
The general approach to solving such problem it to try and eliminate variables (while being careful to not divide by zero). You could have used $A_0 = 2 - A_1$ and then try to find $A_1$ in terms of $X_1$ from second equation. I say $A_1$ because when you go to third equation you have $X_1^2$ but only $A_1$. This means if you had to substitute for $X_1$, you will be required to square a term, which will only increase the work. Which way to proceed usually comes from trial and error and experience.