SOLUTION: How can I solve the following set of equations by using Gauss Elimination Method; 2x + 3y + 4z = 12 3x + y + z = 4 x + 4y + z = 5

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Question 1140942: How can I solve the following set of equations by using Gauss Elimination Method;
2x + 3y + 4z = 12
3x + y + z = 4
x + 4y + z = 5
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

2x+%2B+3y+%2B+4z+=+12
3x+%2B+y+%2B+z+=+4
x+%2B+4y+%2B+z+=+5


Your matrix


Find the pivot in the 1st column and swap the 3rd and the 1st rows:



Eliminate the 1st column:




Make the pivot in the 2nd column by dividing the 2nd row by -11:





Eliminate the 2nd column:



Make the pivot in the 3rd column by dividing the 3rd row by 32%2F11:



Eliminate the 3rd column:



Solution set:
x+=+11%2F32
y=+9%2F16
z=+77%2F32