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 -2



Add Row 1 to Row 2



Divide Row 1 by -2




Multiply Row 1 by -3




Add Row 1 to Row 3



Divide Row 1 by -3



Multiply Row 1 by -1



Add Row 1 to row 4





Divide Row 1 fo -1



Multiply row 2 by -1




Add row 2 to row 3



Multiply Row 2 by 3 and Row 4 by 5



Add Row 2 to Row 4



Swap rows 3 and 4




Now we have only 0's under the diagonal,
so we put the letters and the equal signs back in-



Erase all the 0's and the 1's




Solve the 4th equation for z




Substitute  into the 3rd equation and solve for w





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









Substitute , , and 





So the solution is (x,y,w,z) = (-1,3,-2,2)

Edwin