The idea of elimination is to convert 3 equations with 3 variables to 2 equations with 2 variables, then to 1 equation with 1 variable.

# Solving 3 variable systems of equations by elimination

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Examples

**Solving Three Variable Systems of Equations by Elimination – (Easy)**Solve the following system of equations by elimination:

$x - 4y + z = -12$

$x + 3y - z = 6$

$2x - 2y + z = 5$

**Solving Three Variable Systems of Equations by Elimination – (Medium)**Solve the following system of equations by elimination:

$4x - 3y + 2z = 20$

$-2x - 4y + 3z = 3$

$x + y - z = 2$

**Solving Three Variable Systems of Equations by Elimination – (Hard)**Solve the following system of equations by elimination:

$x + 4y + 7z = 109$

$4x - 5y + 4z = -29$

$5x + y - z = 10$