SOLUTION: How do you solve a linear equations with Gaussian elimination? x+ y + Z =9 2X- 3y +4z =7 X- 4y + 3Z =-2

Multiply row 1 thru by -2 and add to row 2



Multiply row 1 by -1 and add to row 3



Multiply row 2 by -1 and add to row 3



Now we write the system of equations that this
matrix represents:



The bottom equation is all 0's so any values of
x, y, and z would be solutions to it, so we eliminate
it

Choose an arbitrary value for z, we will use 

Or, after erasing the 0s and 1 coefficients:



Substitute  for  in the 2nd equation:



Solve for y





Substitute  for  and  
for  in the first equation:







Clear of fractions:









So the solution is:

(x, y, z) = (,,) 

Edwin