SOLUTION: Plsss solve the System... thanx..... x + y + z - 2w = -4 2y + z + 3w = 4 2x+ y - z + 2w = 5 x

SOLUTION: Plsss solve the System... thanx..... x + y + z - 2w = -4 2y + z + 3w = 4 2x+ y - z + 2w = 5 x - y + w = 4

Question 447917: Plsss solve the System... thanx.....
x + y + z - 2w = -4
2y + z + 3w = 4
2x+ y - z + 2w = 5
x - y + w = 4
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!

 x +  y + z - 2w = -4
     2y + z + 3w =  4
2x +  y - z + 2w =  5
 x -  y     +  w =  4

z is already eliminated in the 4th equation,
Add the 1st and 3rd equation to eliminate z

 x +  y + z - 2w = -4
2x +  y - z + 2w =  5
---------------------
3x + 2y          =  1

Add the 2nd and 3rd equation to eliminate z
 
     2y + z + 3w =  4
2x +  y - z + 2w =  5
---------------------
2x + 3y     + 5w =  9

So now we have this system of equations
in only x, y, and w.  Not z:

 x -  y +  w =  4
3x + 2y      =  1
2x + 3y + 5w =  9

w is already eliminated from the 2nd
equation, so multiply the 1st equation
by -5 and add it to the 3rd equation:

-5x + 5y - 5w = -20
 2x + 3y + 5w =   9
-------------------
-3x + 8y      = -11

So now we have this system of equations
in only x and y.  Not z or w:
  
 3x + 2y =   1
-3x + 8y = -11
----------------
     10y = -10
       y =  -1

Substitute  y = -1 in

    3x + 2y = 1
 3x + 2(-1) = 1
     3x - 2 = 1
         3x = 3
          x = 1

Substitute x = 1 and y = -1 in

   x - y + w = 4
1 - (-1) + w = 4
   1 + 1 + w = 4
       2 + w = 4
           w = 2

Substitute x = 1, y = -1, and w = 2 in

      x + y + z - 2w = -4
 1 + (-1) + z - 2(2) = -4  
       1 - 1 + z - 4 = -4
               z - 4 = -4
                   z = 0

(x,y,z,w) = (1,-1,0,2)

Edwin

RELATED QUESTIONS
x+y+z-2w=2 2y+z+3w=4 2x+y-z+2w=5 x-y... (answered by stanbon)

Use the elimination method to solve the system of equation that has four variables.... (answered by Alan3354)

Please solve for w, x, y, and z. 1. x + 3w = 4 2y - z -w = 0 3y - 2w = 1 (answered by CharlesG2)

This is about Gauss/Jordan Elimination.What are the value of x,y,w and z in the given... (answered by Edwin McCravy)

Solve w+x-y+z=0 w-2x-2y-z=5 w-3x-y+z=4... (answered by Edwin McCravy)

w+x-y+z=0 w-2x-2y-z=-5 w-3x-y+z=4 2w-x-y+3z=7 find the four variables and please show (answered by Alan3354)

2w+x-3y+z=4 w-3x+y+z=32 -w+2x+2y-z=-10... (answered by Fombitz,Alan3354)

what are the values of w,x,y, and z in these equations? 1. w + x + y + z = 2 2. 2w -... (answered by ankor@dixie-net.com)

How would you solve the 4x4 w+x+y+z=2, 2w-x-y+2z=7, 2w+3x+2y-z=-2,... (answered by Fombitz)