Algebra 2 help 10 points

Can you help me how to slove this
Question. Use an augmented matrix to solve linear system
3x+2y=2
5x-6y=50 using a matrix

First, create the matrix, using the coefficients of the terms as the entries, augmented with the solution side:

3 2 | 2
5 -6 | 50

First, divide the first row by 3:

1 2/3 | 2/3
5 -6 | 50

Now, subtract 5 times the first row from the second:

1 2/3 | 2/3
0 -28/3 | 140/3

Multiply the second row by -3/28:

1 2/3 | 2/3
0 1 | -5

Finally, subtract 2/3 row 2 from row 1:

1 0 | 4
0 1 | -5

So, from here, the solution is: x = 4, y = -5