Suppose we have a pairs of simultaneous linear equations

(1)

(2)

We can subtractto give

we can subtractto give

We can represent write the simultaneous equations in matrix form as

Multiplying on the left by the inverse of the matrixwhich equalsgives

This is the same as the solution above.

Example: Use matrices to solve the simultaneous equations

In matrix form this is

The inverse of the matrixis