Can someone help with a chemistry problem?

[Guey G]

can someone please help me understand the algebraic way to balancing equations?

http://www.chembuddy.com/?left=balancing-stoichiometry&right=algebraic-method

i need help with understanding how they get from step to step. like how they got the equation for boron in that particular problem. thanks.

[rhsaunders]

If the equation is balanced, there will be the same number of atoms of each element on each side. Simple example: start with the unbalanced equation Al + Cl2 -> AlCl3. Assign arbitrary coefficients, say P, Q, and R, to get: P Al + Q Cl2 -> R AlCl3. What do we know?
- There is one aluminum on each side, so P = R.
- Chlorine can be in balance only if 3Q = 2R. For example, if Q = 4 and R = 6 (which fits), there will be twelve chlorine atoms on each side.
- We can assign any one coefficient to be a small integer. In this case, we'll arbitrarily let P = 1.
We now have a simple linear system, which when solved yields P = 1, Q = 3/2, and R = 1. Since everything is proportional, we can double all of these to get rid of the fraction, getting 2Al + 3Cl2 -> 2AlCl3.