This math problem is a toughy!! help!!?

Question

x+4y-z=10
-2x+3y-2z=7
3x+2y+z=4


I have gotten 3 different answers.. the answers work for 2 of the equations but not all three.. can someone help??

Answer 1

x + 4y - z = 10
z = x + 4y - 10

-2x + 3y - 2z = 7
-2x + 3y - 2(x + 4y - 10) = 7
-2x + 3y - 2x - 8y + 20 = 7
-4x - 5y = -13
4x + 5y = 13

3x + 2y + z = 4
3x + 2y + x + 4y - 10 = 4
4x + 6y = 14

4x + 5y = 13
4x + 6y = 14
----------------
y = 1
4x = 8
x = 2
z = x + 4y - 10
= 2 + 4 - 10
= -4

x = 2
y = 1
z = -4

Answer 2

x = 2, y = 1, z = -4

Answer 3

Hello,

Add the first and last giving us

4x + 6y = 14

double the third one and add it to the second one

4x + 7y = 15

now subtract these

y = 1

so x = 2

Then put these into the first one

2 + 4*1 -z = 10

-z = 4 so z = -4

Don't forget to check in the original equations.
Hope This Helps!