Question

Solve the following system. If the​ system's equations are dependent or if there is no​ solution, state this.

x - 3z = 9

y + 2z = 0

7x - 3y - 5z = 19

The solution is... ( _, _,_)

Answer 1

Augmented matrix for given system of equations

solution using Gauss-Jordan elimination

Your matrix

	X1	X2	X3	b
1	1	0	-3	9
2	0	1	2	0
3	7	-3	-5	19

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

	X1	X2	X3	b
1	1	0	-3	9
2	0	1	2	0
3	7	-3	-5	19

Eliminate the 1st column

	X1	X2	X3	b
1	1	0	-3	9
2	0	1	2	0
3	0	-3	16	-44

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

	X1	X2	X3	b
1	1	0	-3	9
2	0	1	2	0
3	0	-3	16	-44

Eliminate the 2nd column

	X1	X2	X3	b
1	1	0	-3	9
2	0	1	2	0
3	0	0	22	-44

Make the pivot in the 3rd column by dividing the 3rd row by 22

	X1	X2	X3	b
1	1	0	-3	9
2	0	1	2	0
3	0	0	1	-2

Eliminate the 3rd column

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

Solution set:

x = 3

y = 4

z = -2

The solution is... ( 3 , 4 , -2 )