# How do you solve #[(2x+y),(x-3y)]=[(5), (13)]#?

##### 2 Answers

Create and augmented matrix and the perform row operations until you obtain an identity matrix on the left of the divide.

#### Explanation:

The matrix of coefficients is:

The matrix of constant terms is:

The method that I use is to make an Augmented Matrix

And then perform Elementary Row Operations until I obtain an Identity Matrix on the left side of the divide.

We have obtained an identity matrix.

The values of the unknowns can be read on the right:

Check:

This checks

The answer is

#### Explanation:

We rewrite the equation in matrix form

Let

We calculate

We start by calculating

the matrix of cofactor

Then, we calculate the transpose

The inverse is

Verification

Therefore,