Solve by eliminating variables:

A system of equations consists of two or more equations with the same variables. The solution to the system is the set of values that satisfy all equations simultaneously. In this case, we have three equations with three variables (x, y, z), and we aim to find a common solution that works for all three.

The elimination method is a technique used to solve systems of equations by removing one variable at a time. This is achieved by adding or subtracting equations to eliminate a variable, allowing for simpler equations to be formed. Once one variable is isolated, it can be substituted back into the remaining equations to find the other variables.

Substitution is a method used in solving systems of equations where one variable is expressed in terms of the others. After eliminating a variable, the resulting equations can be solved for one variable, which can then be substituted back into the original equations to find the values of the remaining variables. This method is often used in conjunction with elimination.