 # Solving 3×3 Systems of Equations using Matrices

Related Topics:
More Algebra Lessons
More Lessons on Matrices

Videos, solutions, worksheets, games and activities to help Algebra students learn how to solve 3×3 systems of equations using the inverse of matrices.

We also have a matrix calculator that you can use to calculate the inverse of a 3×3 matrix.

How to solve a system of three linear equations with three unknowns using a matrix equation?
Example:
Solve the system using a matrix equation. (Use a calculator)
x + 2y - z = 7
2x - 3y - 4z = -3
x + y + z = 0
Solving 3-Variable Systems
Matrix Method
Solving a system of equations with 3 variables.
Example:
4x + 2y - 2z = 10
2x + 8y + 4z = 32
30x + 12y - 4z = 24
Solving systems of Equations using Matrices
Using Inverse Matrices to evaluate a system of equations. (Use a calculator)
Example:
3x - 2y + z = 24
2x + 2y + 2z = 12
x + 5y - 2z = -31

Matrix Equations to solve a 3x3 system of equations
Example:
Write the matrix equation to represent the system, then use an inverse matrix to solve it. (Use a calculator)
5x - 2y + 4x = 0
2x - 3y + 5z = 8
3x + 4y - 3z = -11
Solving a 3 × 3 System of Equations Using the Inverse
Example:
Solve the system of equations using an inverse matrix. (Don't use a calculator)
x + 2y + 2z = 5
3x - 2y + z = 6
2x + y - z = -1
This is a calculator that can help you find the inverse of a 3×3 matrix.

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