Press MATRX, and select EDIT (using the right arrow)
ENTER, 2, ENTER, 3, ENTER to define the dimensions of your matrix
Enter each matrix element.  After typing each element, press ENTER.
This defines the matrix [A].

We will do a series of elementary row operations on the matrix [A] defined above to place it in row-echelon form (by forward elimination) and then reduced row-echelon form (by backward elimination).  We assume [A] has already been defined, as shown above.
 

Forward Elimination
MATRIX
Row operation:  Get a 1 in upper left-hand corner byR1ßà R2
Select MATH (right arrow), then select rowSwap (down arrow to #8).
ENTER, then MATRX, ENTER (to select matrix [A])
, 1, 2) ENTER You now see matrix [A] with its rows swapped.
Save (store) this matrix (as [A]) to prepare for the next operation.  STO MATRX ENTER ENTER
Row operation:  Make the 3 a 0 by -3R1 + R2à R2
MATRIX, select MATH, select *row+ (#A), ENTER
-3, MATRX ENTER,1,2)
STO MATRX ENTER ENTER
Row operation:  Make the 10 a 1 by (1/10)R2à R2
MATRX, select MATH, select *row, ENTER .1, MATRX ENTER , 2) ENTER  STO MATRX ENTER ENTER
The matrix is now in row-echelon form.
Backward Elimination
Row operation:  Make the -2 (in row 1) a 1 by 2R2 + R1à R1
MATRX, select MATH, select *row+, ENTER 2, MATRX ENTER , 2, 1) ENTER  STO MATRX ENTER ENTER
The matrix is now in reduced row-echelon form, and the answer is: x = 3, y = -2