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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.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Algebra Lessons

More Lessons on Matrices

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

Example:

Solve the system using a matrix equation. (Use a calculator)

x + 2y - z = 7

2x - 3y - 4z = -3

x + y + z = 0

Matrix Method

Solving a system of equations with 3 variables.

Example:

4x + 2y - 2z = 10

2x + 8y + 4z = 32

30x + 12y - 4z = 24

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

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

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.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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