SOLUTION: Solve the following set of equations by using Gauss Elimination Method. 2x+3y+4z = 12 3x+y+z = 4 x+4y+z = 5

Algebra ->  Linear-equations -> SOLUTION: Solve the following set of equations by using Gauss Elimination Method. 2x+3y+4z = 12 3x+y+z = 4 x+4y+z = 5       Log On


   

Question 1054228: Solve the following set of equations by using Gauss Elimination Method.
2x+3y+4z = 12
3x+y+z = 4
x+4y+z = 5

Found 2 solutions by ewatrrr, Fombitz:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
3x+y+z = 4
-x-4y-z = -5
2x+-+3y+=+-1
2x+3y+4z = 12
-12x-4y-4z = -16
-10x+-+y+=+-4
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2x - 3y = -1
-10x - y = -4
|
2x - 3y = -1
30x + 3y = 12
32x =11
x = 11/32
y= 9/16 y+=+-10x+%2B+4
z = 77/32 z+=+5+-x+-+4y

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply eq. 3 by 2 and subtract from eq. 1,
2x%2B3y%2B4z-2x-8y-2z=12-10
4.-5y%2B2z=2
Multiply eq. 3 by 3 and subtract from eq. 2,
3x%2By%2Bz-3x-12y-3z=4-15
5.+-11y-2z=-11
Add eqs. 4 and 5,
-5y%2B2z-11y-2z=2-11
-16y=-9
y=9%2F16
So then working backwards,
-5%289%2F16%29%2B2z=2
-45%2F16%2B2z=2
2z=32%2F16%2B45%2F16
2z=77%2F16
z=77%2F32
and finally,
x%2B4%289%2F16%29%2B77%2F32=5
x%2B36%2F16%2B77%2F32=160%2F32
x=160%2F32-72%2F16-77%2F32
x=11%2F32