Question 983164
X + 2y + z = 7
X + 3z = 11
2x - 3y = 1
:
Use elimination here, multiply the 3rd equation by -1 and add
X + 2y + z = 7
X + 0y + 3z = 11
-2x + 3y + 0 = -1
-------------------Addition eliminates x
5y + 4z = 17
4z = -5y + 17
divide by 4
z = -1.25y + 4.25
:
Use elimination again on the 1st two equation
X + 0y + 3z = 11
X + 2y + z = 7
----------------subtraction eliminates x again
-2y + 2z = 4
simplify divide by 2
-y + z = 2
z = y + 2
:
z = z, therefore
y + 2 = -1.25y + 4.25
y + 1.25y = 4.25 - 2
2.25y = 2.25
y = 1
then
z = 1 + 2
z = 3
Find x using x + 3z = 11
x + 3(3) = 11
x = 11 - 9
x = 2
:
we have x=2; y=1; z=3
:
Check that in the 1st equation: x + 2y + z = 7, replace xyz 
2 + 2(1) + 3 = 7