# How do you find the values of x and y given #[(27),(8)]=[(3y), (5x-3y)]#?

##### 1 Answer

Write an Augmented matrix and then perform Elementary Row Operations

#### Explanation:

The Coefficient Matrix is:

Before one begins to solve a system of equations, it is best to be sure that the Determinant of the coefficient matrix is not zero:

The determinant is not zero, therefore, the system of equations has a unique solution.

You can write the system using the coefficient matrix multiplied by a Column Vector of unknown variables that is equal equal to a column vector of constants as follows:

And then perform Elementary Row Operations

However, I recommend that you eliminate the column vector of unknowns, and merge the coefficient matrix with the column vector of constants into an Augmented matrix

And then perform Elementary Row Operations

Read the solutions from the right side of the matrix :

Check

This checks.