Your matrix

        X1	X2	X3	X4	b
1	1	0	3	0	2
2	0	1	0	-3	3
3	-2	0	3	2	1
4	3	0	0	7	5

Find the pivot in the 1st column in the 1st row

        X1	X2	X3	X4	b
1	1	0	3	0	2
2	0	1	0	-3	3
3	-2	0	3	2	1
4	3	0	0	7	5

Eliminate the 1st column

        X1	X2	X3	X4	b
1	1	0	3	0	2
2	0	1	0	-3	3
3	0	0	9	2	5
4	0	0	-9	7	-1

Find the pivot in the 2nd column in the 2nd row

        X1	X2	X3	X4	b
1	1	0	3	0	2
2	0	1	0	-3	3
3	0	0	9	2	5
4	0	0	-9	7	-1

Make the pivot in the 3rd column by dividing the 3rd row by 9

        X1	X2	X3	X4	b
1	1	0	3	0	2
2	0	1	0	-3	3
3	0	0	1	2/9	5/9
4	0	0	-9	7	-1

Eliminate the 3rd column

        X1	X2	X3	X4	b
1	1	0	0	-2/3	1/3
2	0	1	0	-3	3
3	0	0	1	2/9	5/9
4	0	0	0	9	4

Make the pivot in the 4th column by dividing the 4th row by 9

        X1	X2	X3	X4	b
1	1	0	0	-2/3	1/3
2	0	1	0	-3	3
3	0	0	1	2/9	5/9
4	0	0	0	1	4/9

Eliminate the 4th column

        X1	X2	X3	X4	b
1	1	0	0	0	17/27
2	0	1	0	0	13/3
3	0	0	1	0	37/81
4	0	0	0	1	4/9


Solution set:

x1 = 17/27
x2 = 13/3
x3 = 37/81
x4 = 4/9