Question

find a 3x3 solution using substitution

5x-2y+3z=20

2x-4y-3z=-9

x+6y-8z=21

Answer 1

Augmented matrix for given system of equations

Your matrix

	X1	X2	X3	b
1	5	-2	3	20
2	2	-4	-3	-9
3	1	6	-8	21

Find the pivot in the 1st column and swap the 3rd and the 1st rows

	X1	X2	X3	b
1	1	6	-8	21
2	2	-4	-3	-9
3	5	-2	3	20

Eliminate the 1st column

	X1	X2	X3	b
1	1	6	-8	21
2	0	-16	13	-51
3	0	-32	43	-85

Make the pivot in the 2nd column by dividing the 2nd row by -16

	X1	X2	X3	b
1	1	6	-8	21
2	0	1	-13/16	51/16
3	0	-32	43	-85

Eliminate the 2nd column

	X1	X2	X3	b
1	1	0	-25/8	15/8
2	0	1	-13/16	51/16
3	0	0	17	17

Make the pivot in the 3rd column by dividing the 3rd row by 17

	X1	X2	X3	b
1	1	0	-25/8	15/8
2	0	1	-13/16	51/16
3	0	0	1	1

Eliminate the 3rd column

	X1	X2	X3	b
1	1	0	0	5
2	0	1	0	4
3	0	0	1	1

Solution set:

x = 5

y = 4

z = 1