Question

Solve this system of equations. Write the solution as an ordered triple.
6x + 3y + z = 36
x - 3y + 2z = -12
17x - 2y + 3z = 80

Answer 1

Augmented matrix for given system of equations

solution using Gauss-Jordan elimination

Your matrix

	X1	X2	X3	b
1	6	3	1	36
2	1	-3	2	-12
3	17	-2	3	80

Find the pivot in the 1st column and swap the 2nd and the 1st rows

	X1	X2	X3	b
1	1	-3	2	-12
2	6	3	1	36
3	17	-2	3	80

Eliminate the 1st column

	X1	X2	X3	b
1	1	-3	2	-12
2	0	21	-11	108
3	0	49	-31	284

Make the pivot in the 2nd column by dividing the 2nd row by 21

	X1	X2	X3	b
1	1	-3	2	-12
2	0	1	-11/21	36/7
3	0	49	-31	284

Eliminate the 2nd column

	X1	X2	X3	b
1	1	0	3/7	24/7
2	0	1	-11/21	36/7
3	0	0	-16/3	32

Make the pivot in the 3rd column by dividing the 3rd row by -16/3

	X1	X2	X3	b
1	1	0	3/7	24/7
2	0	1	-11/21	36/7
3	0	0	1	-6

Eliminate the 3rd column

	X1	X2	X3	b
1	1	0	0	6
2	0	1	0	2
3	0	0	1	-6

Solution set:

x = 6

y = 2

z = -6

Ordered triple (x , y , z ) = ( 6 , 2 , -6 )