The substitution or addition methods can also be used to solve a system of three linear equations in three variables. Consider the following system.

  x + y + z = 7

 x - y + 2z = 9

-x + 2y + z = 4

The ordered triple (x, y, z) is the solution to the system if it satisfies all three equations.

(a) Show that the ordered triple (2, 1, 4) is a solution to the system.

(b) Use the substitution or addition method to determine the solution to the system (Eliminate one variable by using two equations. Then eliminate the same variable by using two different equations.)