# How to solve simultaneous equations in 3 variables

The method shows one how to solve 3 simultaneous equations as below for x, y, z

Problem is to the solve the following simultaneous equations

22x + 5y + 7z = 12 (1)

10x + 3y + 2z = 5 (2)

9x + 2y + 12z = 14 (3)

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#### Solution Preview

Methodology to solve simultaneous Equations containing three variables

Problem is to the solve the following simultaneous equations

22x + 5y + 7z = 12 (1)

10x + 3y + 2z = 5 (2)

9x + 2y + 12z = 14 (3)

From (2) we can multiply both sides by 6 to get

60x + 18y + ...

#### Solution Summary

A detailed example showing how to solve simultaneous equations in 3 variables using addition/subtraction and substitution methods.

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