Solve the equation system:
We choose to solve the simultaneous equations by using the substitution method and begin by solving for a variable from one of the equations. It doesn't matter which variable or which equation you choose, so we will start by solving for
from the third equation.
We use this expression to replace in both of the other equations and simplify.
Now that has been removed from equation (I) and (II), they now make a system of equations with only two unknowns.
We choose to solve this by using the addition method, but we could just as well have chosen the substitution method. By changing the sign of the bottom equation and then multiplying by , the -terms cancel each other out when added.
We have now solved for and . We can then put them in equation (III) in order to finally solve for .
Now we have solved for all the unknown variables and the solutions are