SOLUTION: how do i solve the following 4 x 4 system using elimination & substitution? w + 2x + 2y + z = -2 w + 3x - 2y - z = -6 -2w - x + 3y + 3z = 6 w + 4x + y - 2z = -14

Algebra ->  Equations -> SOLUTION: how do i solve the following 4 x 4 system using elimination & substitution? w + 2x + 2y + z = -2 w + 3x - 2y - z = -6 -2w - x + 3y + 3z = 6 w + 4x + y - 2z = -14      Log On


   

Question 1059434: how do i solve the following 4 x 4 system using elimination & substitution?
w + 2x + 2y + z = -2
w + 3x - 2y - z = -6
-2w - x + 3y + 3z = 6
w + 4x + y - 2z = -14
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
R%5B1%5D:w+%2B+2x+%2B+2y+%2B+z++=+-2
R%5B2%5D:w+%2B+3x+-+2y+-+z+=++-6
R%5B3%5D:-2w+-+x+%2B+3y+%2B+3z+=++6
R%5B4%5D:+w+%2B+4x+%2B+y+-+2z+=++-14
Eliminate w by using elementary row operations,
R%5B1%5D-R%5B2%5D:w+%2B+2x+%2B+2y+%2B+z+-w+-+3x+%2B+2y+%2B+z+=-2-%28-6%29
R%5B1%5D-R%5B2%5D:-x%2B4y%2B2z=+4
.
.
2R%5B1%5D%2BR%5B3%5D:2w%2B4x%2B2y%2B2z-2w-x%2B3y%2B3z=-4%2B6
2R%5B1%5D%2BR%5B3%5D:3x%2B7y%2B5z=2
.
.
R%5B1%5D-R%5B4%5D:w+%2B+2x+%2B+2y+%2B+z-w-4x-y%2B2z=-2-%28-14%29
R%5B1%5D-R%5B4%5D:-2x%2By%2B3z=12
So now your reformed equations are,
R%5B5%5D:-x%2B4y%2B2z=+4
R%5B6%5D:3x%2B7y%2B5z=2
R%5B7%5D:-2x%2By%2B3z=12
Continue in this fashion until you have solved for one variable and then work backwards.
You can eliminate x by these row operations,
3R%5B5%5D%2BR%5B6%5D and
-2R%5B5%5D%2BR%5B7%5D