SOLUTION: I am having trouble with my college homework sheets. Can someone please help me figure these out. I would really appreciate all the help you can give me. This problem is from homew

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Question 138631: I am having trouble with my college homework sheets. Can someone please help me figure these out. I would really appreciate all the help you can give me. This problem is from homework sheet
16.) 6x-y-5z=27
-8x +2z=-56
4y + z=8
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
16.) we can arrange it like this:
6x - y - 5z = 27; eq:1
-8x + 0y +2z =-56; eq:2
0x + 4y + z = 8: eq:3
:
Mult eq 3 by 5 and add it to eq1
6x - y - 5z = 27
0x +20y +5z = 40
--------------------adding eliminates z:
6x + 19y = 67
:
Mult eq 3 by 2 and subtract from eq2
-8x+ 0y + 2z = -56
0x + 8y + 2z = 16
--------------------Subtracting eliminates z again
-8x - 8y = -72
Divide equation by -8, resulting in
x + y = 9
y = (9-x); use for substitution in the equation: 6x + 19y = 47:
6x + 19(9-x) = 67
6x + 171 - 19x = 67
6x - 19x = 67 - 171
-13x = -104
x = %28-104%29%2F%28-13%29
x = +8
:
y = 9 -x
y = 9 - 8
y = +1
:
Use eq3 to find z, substitute for 1 for y:
4(1) + z = 8
z = 8 - 4
z = +4
:
Our solutions: x=8; y=1; z=4
:
Check solutions in eq1
6x - y - 5z = 27
6(8) - 1 - 5(4) =
48 - 1 - 20 = 47; confirms our solutions