How do you solve linear equations in three variables?

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.

''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.''