How do you solve linear equations in three variables?

''Pick any two pairs of equations from the system. Eliminate the same variable from each pair using the Addition/Subtraction method. Solve the system of the two new equations using the Addition/Subtraction method.''

Really depends upon the 3 equations.
If you can find x in terms of y and z in one of the problems,
then substitute this back into the other two equations, then solve the 2 equations and two unknowns.
There are other elimination techniques but difficult to explain.
Or use the matrix solution technique in the TI calculator and use "rrde" to solve.