These lessons, with videos, examples, solutions, worksheets and activities, 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.

**Related Pages**

Solving a System of Equations

Inverse Matrix

Types Of Matrices

More Lessons On Matrices

More Lessons for Grade 9

More Algebra Lessons

**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

**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

**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

**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

This is a calculator that can help you find the inverse of a 3×3 matrix.

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

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.