Question

Solve, find x y and z:

6x+8y-6z=62

10x-12y-14z=14

12x-8y+20z=-68

Answer 1

Augmented matrix for given system of equations

Your matrix

	X1	X2	X3	b
1	6	8	-6	62
2	10	-12	-14	14
3	12	-8	20	-68

Make the pivot in the 1st column by dividing the 1st row by 6

	X1	X2	X3	b
1	1	4/3	-1	31/3
2	10	-12	-14	14
3	12	-8	20	-68

Eliminate the 1st column

	X1	X2	X3	b
1	1	4/3	-1	31/3
2	0	-76/3	-4	-268/3
3	0	-24	32	-192

Make the pivot in the 2nd column by dividing the 2nd row by -76/3

	X1	X2	X3	b
1	1	4/3	-1	31/3
2	0	1	3/19	67/19
3	0	-24	32	-192

Eliminate the 2nd column

	X1	X2	X3	b
1	1	0	-23/19	107/19
2	0	1	3/19	67/19
3	0	0	680/19	-2040/19

Make the pivot in the 3rd column by dividing the 3rd row by 680/19

	X1	X2	X3	b
1	1	0	-23/19	107/19
2	0	1	3/19	67/19
3	0	0	1	-3

Eliminate the 3rd column

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

Solution set:

x = 2

y = 4

z = -3