Question

Solve the following system. If the system's equations are dependent or if there is no solution, state this.
3x - 4y - z = 18
4x + 2y + z = 16
7x - 2y + 3z = 19

Answer 1

Augmented matrix for given system of equations

solution using Gauss-Jordan elimination

Your matrix

	X1	X2	X3	b
1	3	-4	-1	18
2	4	2	1	16
3	7	-2	3	19

Make the pivot in the 1st column by dividing the 1st row by 3

	X1	X2	X3	b
1	1	-4/3	-1/3	6
2	4	2	1	16
3	7	-2	3	19

Eliminate the 1st column

	X1	X2	X3	b
1	1	-4/3	-1/3	6
2	0	22/3	7/3	-8
3	0	22/3	16/3	-23

Make the pivot in the 2nd column by dividing the 2nd row by 22/3

	X1	X2	X3	b
1	1	-4/3	-1/3	6
2	0	1	7/22	-12/11
3	0	22/3	16/3	-23

Eliminate the 2nd column

	X1	X2	X3	b
1	1	0	1/11	50/11
2	0	1	7/22	-12/11
3	0	0	3	-15

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

	X1	X2	X3	b
1	1	0	1/11	50/11
2	0	1	7/22	-12/11
3	0	0	1	-5

Eliminate the 3rd column

	X1	X2	X3	b
1	1	0	0	5
2	0	1	0	1/2
3	0	0	1	-5

Hide solution

Recalculate

Solution set:

x = 5

y = 1/2

z = -5