Question

Solve using both Gaussian Elimination (row operations) and also Cramer’s Rule

x + 3y - 6z = 7

2x - y + 2z = 0

x + y + 2z = -1

Answer 1

1	3	-6	7
2	-1	2	0
1	1	2	-1

convert into Reduced Row Eschelon Form...

Add (-2 * row1) to row2

1	3	-6	7
0	-7	14	-14
1	1	2	-1

Add (-1 * row1) to row3

1	3	-6	7
0	-7	14	-14
0	-2	8	-8

Divide row2 by -7

1	3	-6	7
0	1	-2	2
0	-2	8	-8

Add (2 * row2) to row3

1	3	-6	7
0	1	-2	2
0	0	4	-4

Divide row3 by 4

1	3	-6	7
0	1	-2	2
0	0	1	-1

Add (2 * row3) to row2

1	3	-6	7
0	1	0	0
0	0	1	-1

Add (6 * row3) to row1

1	3	0	1
0	1	0	0
0	0	1	-1

Add (-3 * row2) to row1

1	0	0	1
0	1	0	0
0	0	1	-1

2 2 3 2 2 2 t+21 づ (10,-1) 28

solution is

$\large {\color{Red} (x,y,z)=(1,0,-1)}$