Put in all the 1's



Erase the letters and the plus signs,
put a bar where the equal signs are, 
and put the whole thing in parentheses:



The idea is to get all 0's below the diagonal.

Caution: 

1. After you've finished getting zeros under the diagonal
in column 1, NEVER USE ROW 1 AGAIN!
2. After you've finished getting zeros under the diagonal
in column 2, NEVER USE ROW 2 AGAIN!

Multiply the Row 1 by -4



Add Row 1 to Row 2



Divide Row 1 by -4



Multiply Row 1 by 3



Add Row 1 to Row 3



Divide Row 1 by -3



Add Row 1 to row 4



Multiply Row 4 by 2



Add Row 3 to Row 4



Divide Row 3 by 2
Divide Row 4 by 2

 


Multiply Row 2 by 4
Multiply Row 3 by 11



Add Row 2 to Row 3



Multiply Row 4 by 3
Divide Row 2 by 4



Add Row 3 to Row 4



Now put the letters and the equal signs back in-



Erase all the 0's and the 1's



Solve the 4th equation for w




Substitute  into the 3rd equation and solve for z






Substitute  and  into the 2nd 
equation and solve for y:









Substitute , , and 






So the solution is (x,y,z,w) = (0,1,-2,4)

Edwin