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.


  1. Image titled 1109151928
    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.
      Image titled 1109151929a
  2. Image titled 1109151930
    Find the opposite matrix, which is a and d switched, and then the signs switched on b and c.
  3. Image titled 1109151949
    Find the inverse matrix. To do this, you need to solve for 1 over ab-cd times the opposite matrix.
  4. Image titled 1109151957
    Image titled 1109151950a
    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