Algebraic Solution of Linear Equations in 3 Unknowns
Algebraic Solution of Linear Equations in 3 Unknowns
Introduction to Linear Equations in Three Variables

Linear equations can be expanded to include three variables, primarily represented as x, y, and z.

An example of a linear equation in three variables is: ax + by + cz = d, where a, b, c, and d are constants.
Formulation of Linear Equations in Three Variables

The formation of linear equations in three variables follows the same principles as for two variables.

The difference is that there is now an additional z term that needs to be incorporated into the formation and solution of the equations.
Solving Linear Equations in Three Variables

The main goal when solving linear equations in three variables is to use substitution and elimination methods to find the values of x, y, and z.

To eliminate one of the variables, it is common to add or subtract the equations.

Once one variable is eliminated, a system of two equations will be left, which can be solved using wellknown twovariable methods.
Checking the Solution for Accuracy

After obtaining a solution, it is important to check the values that were found for x, y, and z by substituting them back into the original equations.

If the substituted values hold true for all of the original equations, then the solution can be considered as valid.