How do you solve a set of three similatenous equations with three unknown variables?

You should manipulate the equations into a form where you can eliminate a variable, using two of the equations. From here, you should be left with two new equations and two unknown variables. Repeat the same again, manipulating the equations (by this I mean getting the co-efficients of one of the variables the same, and use the rules 'same sign subtract' or 'opposite signs add') to eliminate a variable. Once you have two of the three unknowns, you can plug the numbers back into one of the original equations and compute the last unknown variable.