Question

Solve:

4x - 3z = 1

-3x - z = -3

2x + y + z = -1

Answer 1

Augmented matrix for given system of equations

solution using Gauss-Jordan elimination

Your matrix

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

Make the pivot in the 1st column by dividing the 1st row by 4

	X1	X2	X3	b
1	1	0	-0.75	0.25
2	-3	0	-1	-3
3	2	1	1	-1

Eliminate the 1st column

	X1	X2	X3	b
1	1	0	-0.75	0.25
2	0	0	-3.25	-2.25
3	0	1	2.5	-1.5

Find the pivot in the 2nd column and swap the 3rd and the 2nd rows

	X1	X2	X3	b
1	1	0	-0.75	0.25
2	0	1	2.5	-1.5
3	0	0	-3.25	-2.25

Make the pivot in the 3rd column by dividing the 3rd row by -3.25

	X1	X2	X3	b
1	1	0	-0.75	0.25
2	0	1	2.5	-1.5
3	0	0	1	9/13

Eliminate the 3rd column

	X1	X2	X3	b
1	1	0	0	10/13
2	0	1	0	-4213
3	0	0	1	9/13

Solution set:

x = 10/13

y = -42/13

z = 9/13