Question

4x-2y-2z=2
-x-5y+2z=-8
4x-5y+z=11

Please make sure you show all steps numerically, becuse I want to be sure I know how to arrive at the same numbers.

Answer 1

4	-2	-2		2
-1	-5	2		-8
4	-5	1		11

multiply the 1st row by 1/4

1	-1 / 2	-1 / 2		1/ 2
-1	-5	2		-8
4	-5	1		11

add 1 times the 1st row to the 2nd row

1	-1 / 2	-1 / 2		1/ 2
0	-11 / 2	3 / 2		-15 / 2
4	-5	1		11

add -4 times the 1st row to the 3rd row

1	-1 / 2	-1 / 2		1 / 2
0	-11 / 2	3 / 2		-15 / 2
0	-3	3		9

multiply the 2nd row by -2/11

1	-1 / 2	-1 / 2		1 / 2
0	1	-3 / 11		15 /11
0	-3	3		9

add 3 times the 2nd row to the 3rd row

1	-1/ 2	-1 / 2		1 / 2
0	1	-3 / 11		15/ 11
0	0	24 /11		144 / 11

multiply the 3rd row by 11/24 1 -1/ 2 -1 / 2 1 / 2 0 1 -3 / 11 15 / 11 0 0 1 6

add 3/11 times the 3rd row to the 2nd row

1	-1 / 2	-1 / 2		1 / 2
0	1	0		3
0	0	1		6

add 1/2 times the 3rd row to the 1st row 1 -1 / 2 0 7 / 2 0 1 0 3 0 0 1 6 add 1/2 times the 2nd row to the 1st row 1 0 0 5 0 1 0 3 0 0 1 6 Hence x = 5, y = 3, z = 6