For simple problems, using the algebraic method of solving chemical equations has always been relatively easy.

Find the equations for each element, set a=1, solve for another variable, use that variable to solve for another, and so on down the line.

But it's harder for me now, because the problems are getting more complex.

Like this one: CaCO_{3}+CH_{3}COOH---------->Ca(CH_{3}COO)_{2}+H_{2}O+CO_{2}

Now when I try to solve, I get the following equations:

Ca: a=c

C: a+2b=4c+e

O: 3a+2b=4c+d+2e

H: 4b=6c+2d

Now I set a=1, and therefore I find c (as per the first equation), but the rest of the coefficients are harder to solve for. Which coefficients should I solve for first, and why? And how do I go about doing this?