SOLUTION: Hi, I have worked this problem over and over, but I can't seem to get it right. The directions are to solve using the elimination method. Thanks for your help! 4x-y+2z=-18 -x+

Algebra ->  College  -> Linear Algebra -> SOLUTION: Hi, I have worked this problem over and over, but I can't seem to get it right. The directions are to solve using the elimination method. Thanks for your help! 4x-y+2z=-18 -x+      Log On


   

Question 499998: Hi, I have worked this problem over and over, but I can't seem to get it right. The directions are to solve using the elimination method. Thanks for your help!
4x-y+2z=-18
-x+2y+z=11
3x+3y-4z=44
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
4x - y + 2z =-18
-x+ 2y + z =11
3x+ 3y- 4z =44
:
Multiply the last equation by -1
4x - y + 2z =-18
-x+ 2y + z = 11
-3x-3y + 4z =-44
--------------------addition eliminates x
0 - 2y + 7z = -51
:
multiply the 2nd equation by 3, add to the 3rd equation
-3x+ 6y + 3z = 33
3x + 3y - 4z = 44
--------------------Addition eliminates x
0 + 9y - z = 77
Multiply this eq by 7, add to the other 2 unknown equation
63y - 7z = 539
-2y + 7z = -51
---------------------addition eliminates z find y
61y = 488
y = 488%2F61
y = 8
:
Find z using: -2y + 7z = -51
-2(8) + 7z = -51
-16 + 7z = -51
7z = -51 + 16
7z = -35
z = %28-35%29%2F7
z = -5
:
Find x using the 3rd original equation; 3x + 3y - 4z = 44
3x + 3(8) - 4(-5) = 44
3x + 24 + 20 = 44
3x + 44 = 44
3x = 44 - 44
3x = 0
x = 0
:
Summarize: x=0; y=8; z=-5
:
Confirm this in the 1st original equation; 4x - y + 2z =-18
4(0) - 8 + 2(-5) = -18
9 - 8 - 10 = -18, OK