Question

3×3 Systems Elimination by Addition

1) -5x-2y+20z=-28
2)   2x-5y+15z=-27
3) -2x-2y-5z= -12

Please write out all of the steps so I'll be able to figure out the formulas myself.

Answer 1

Augmented matrix for given system of equations

solution using Gauss-Jordan elimination

Your matrix

	X1	X2	X3	b
1	-5	-2	20	-28
2	2	-5	15	-27
3	-2	-2	-5	-12

Make the pivot in the 1st column by dividing the 1st row by -5

	X1	X2	X3	b
1	1	2/5	-4	28/5
2	2	-5	15	-27
3	-2	-2	-5	-12

Eliminate the 1st column

	X1	X2	X3	b
1	1	2/5	-4	28/5
2	0	-29/5	23	-191/5
3	0	-6/5	-13	-4/5

Make the pivot in the 2nd column by dividing the 2nd row by -29/5

	X1	X2	X3	b
1	1	2/5	-4	28/5
2	0	1	-115/29	191/29
3	0	-6/5	-13	-4/5

Eliminate the 2nd column

	X1	X2	X3	b
1	1	0	-70/29	86/29
2	0	1	-115/29	191/29
3	0	0	-515/29	206/29

Make the pivot in the 3rd column by dividing the 3rd row by -515/29

	X1	X2	X3	b
1	1	0	-70/29	86/29
2	0	1	-115/29	191/29
3	0	0	1	-2/5

Eliminate the 3rd column

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

Solution set:

x = 2

y = 5

z = -2/5