SOLUTION: 4x - y= 2 3y + z= 9 x + 2z= 7

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Question 906682: 4x - y= 2
3y + z= 9
x + 2z= 7
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
(1)    4x - y = 2
(2)    3y + z = 9
(3)    x + 2z = 7

z is already eliminated in (1),

so eliminate z from (2) and (3)

Solve (2) for z

(2)    3y + z = 9
            z = 9 - 3y

Substitute 9-3y for z in (3)

(3)    x + 2z = 7
  x + 2(9-3y) = 7
  x + 18 - 6y = 7
(4)    x - 6y = -11

Solve the system:

(1)    4x -  y = 2
(4)     x - 6y = -11

Solve (4) for x

             x = -11+6y

Substitute -11+6y for x in (1)

 4(-11+6y) - y = 2    
   -44+24y - y = 2 
           23y = 46
             y = 2

             x = -11+6y
             x = -11+6(2)
             x = -11+12
             x = 1 

Substitute in            

             z = 9 - 3y
             z = 9 - 3(2)
             z = 9 - 6
             z = 3

(x,y,z) = (1,2,3)

Edwin
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