Question

Could someone help me solve these system using elementary operations, I am having trouble with both of them.

x+y+z =0
x-y =1
y-z =-5
(For the one above the answer is (-1,-2,3)

2x-y =0
2y-z =7
2z-x =0
(For the one above the answer is (2,4,1)

Answer 1

first one:

add all 3 equations --> 2x + y = -4
now add this to the second ...
3x = -3
x = -1

sub that onto the second and third to get y and z

"play around" with the second question in a similar way.
I would use substitution,
e.g. for the first ---> y = 2x
from the second z = 2y - 7
z = 2(2x) - 7
= 4x - 7

now in the third
2z - x = 0
2(4x-7) - x = 0
7x = 14
x = 2
Now you can find the other two.