Chapter 7 - Section 7.2 - Systems of Linear Equations in Three Variables - Exercise Set - Page 831: 44

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While there are different ways of solving a system in three variables, we can usually eliminate one variable (say $z$) by substitution and reduce the system to two variables. Repeat the elimination process to find the value of one variable (say $x$) and then use back-substitution to find the values of the other two variables.