Question

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

3x - 4y -z = 9

2x + 2y + z = 0

5x - 2y + 2z = -1

The solution is....

PLEASE MAKE SURE THIS IS CORRECT. I KEEP PAYING FOR THE WRONG ANSWER!

Answer 1

Augmented matrix for given system of equations

solution using Gauss-Jordan elimination

Your matrix

	X1	X2	X3	b
1	3	-4	-1	9
2	2	2	1	0
3	5	-2	2	-1

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

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

Eliminate the 1st column

	X1	X2	X3	b
1	1	-4/3	-1/3	3
2	0	14/3	5/3	-6
3	0	14/3	11/3	-16

Make the pivot in the 2nd column by dividing the 2nd row by 14/3

	X1	X2	X3	b
1	1	-4/3	-1/3	3
2	0	1	5/14	-9/7
3	0	14/3	11/3	-16

Eliminate the 2nd column

	X1	X2	X3	b
1	1	0	1/7	9/7
2	0	1	5/14	-9/7
3	0	0	2	-10

Make the pivot in the 3rd column by dividing the 3rd row by 2

	X1	X2	X3	b
1	1	0	1/7	9/7
2	0	1	5/14	-9/7
3	0	0	1	-5

Eliminate the 3rd column

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

Solution set:

x = 2

y = 1/2

z = -5

The solution is.... (x,y,z) = ( 2 , 1/2 , -5) (Answer)