Question 632151
2x + y + z = –7
x – 3y + 4z = –14
x – 2y – 3z = –11
We can use elimination here, Multiply the 1st equation by -1
-2x -y - z = 7
x – 3y + 4z = –14
x – 2y – 3z = –11
---------------------Adding eliminates x and z, find y
0 - 6y = - 18
y = -18/-6
y = +3
:
Find x and z
Use the 2nd and 3rd equations, replace y with 3
x – 3(3) + 4z = –14
x – 2(3) – 3z = –11
:
x - 9 + 4z = -14
x - 6 - 3z = -11
:
x + 4z = -14 + 9
x - 3z = -11 + 6
:
x + 4z = -5
x - 3z = -5
--------------subtraction eliminates x find z
7z = 0
z = 0
therefore
x = -5
:
Check solutions in the 1st original equation
2x + y + z = –7
2(-5) + 3 + 0 = 
-10 + 3 = -7