# How do you solve the system #x+5y=26, 3x-2y=-41# using matrix equation?

##### 1 Answer

Write the two equations as a 2 by 3 augmented matrix.

Use elementary row operations, until an identity matrix is obtained on the left, then the column vector on the right will contain the solution.

#### Explanation:

Use the first equation,

Use the second,

We have the 2 by 3 augmented matrix, therefore, we may begin elementary row operations.

Multiply the first row by -3, add it to the second row, and put the result in the second row:

Divide the second row by -17:

Multiply the second row by -5 and add it to the first row:

We have an identity matrix on the left, therefore, the solution is in the column vector on the right:

Check:

This checks.