Pick an equation and variable to work with first. Ideally, this will be the equation with a lone variable or numbers that are all divisible into one another.
Isolate the variable by subtracting every other variable from the answer to the equation.
Substitute that answer in for the original variable in another equation. This will eliminate that variable from the equation, thus giving you only three variables to solve.
Combine the variables and solve for another variable by isolating it from the rest of the equation.
Substitute that answer in for the newly isolated variable. This will give you an equation with only two variables present.
Combine variables and isolate one of the two variables.
Substitute the new equation into one of the equations. This equation will only have one variable.
Solve for the lone variable and plug it into the two-variable equation to solve for that variable.
Plug both solved variables into the third equation to solve for the third variable.
Substitute all known variables in an equation with all original variables to solve for the last unknown variable.