# How to Solve a System of Linear Equations Using Inverse Matrices

This is a simple guide to solving a 2x2 matrix using the inverse method.

An editor has suggested that this article be merged with: "How to Use Inverse Matrices to Solve Systems of Equations" Per the merge policy, if these topics are determined to be similar but distinct, then the articles will remain separate. Please comment on the discussion page. Notice added on 2016-04-23. |

## Steps

- 1
**Write the equations as a matrix.**Label each matrix as A, X, and C.- If A times X equals C, then A^-1 (the inverse of A) times A times X equals A^-1 times C, then X equals A^-1 times C. This is because A and its inverse cancel each other out.

- 2
**Find the opposite matrix, which is a and d switched, and then the signs switched on b and c.** - 3
**Find the inverse matrix.**To do this, you need to solve for 1 over ab-cd times the opposite matrix. - 4
**Take the inverse matrix and multiply the x and y columns by x and y, respectively.**That will give you your answer.

## Article Info

Categories: Merge | Mathematics