x + y + z = 6 -------- eq (i)

2x - y - z = 3 ------- eq (ii)

x + y - z = 0 -------- eq (iii)

3x = 9 ------- Adding eqs (i) & (ii)

Instead of 2x - y - z = 3, equation (ii) should have been: 2x - y + z = 3 , and so:  

Answer by ikleyn(52908)   (Show Source): You can put this solution on YOUR website!
 .

Solve the system : x + y + z = 6, 2x - y + z = 3, x + y - z = 0

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~





 x + y + z = 6,    (1)
2x - y + z = 3,    (2)
 x + y - z = 0     (3)

Add equations (2) and (3) (both sides). You will get

3x = 3.   Hence, x = 1.

Substitute x = 1 into equations ((1) and (3). You will get

1 + y + z = 6,
1 + y - z = 0,

or, which is the same,

y + z =  5,    (3)
y - z = -1.    (4)

Now add the equations (3) and (4) (both sides). You will get

2y = 4.   Hence, y = 2.

Now from (3) z = 5 - y = 5 - 2 = 3.

Answer.  x = 1,  y = 2,  z = 3.


 

RELATED QUESTIONS

  Solve 
      x + y - z = 0 
    2x - y + z = 6  
    -x + y + z = 8 
Show your... (answered by jim_thompson5910)

  Solve 
      x + y - z = 0 
    2x - y + z = 6  
    -x + y + z = 8 
Show your... (answered by vertciel)

Solve the system:  x + y - z = 2
                  2x + y + z = 3
                  3x... (answered by Alan3354)

solve the system:
 x+y-z=2
2x+y+z=3... (answered by pie90010)

4.  Solve 
      x + y - z = 0 
    2x - y + z = 6  
    -x + y + z = 8 
Show your... (answered by mayank,MathLover1)

Solve the following system.
 	2x + 4y + 3z = 2 
x + 2y - z = 0 
4x + y - z = 6
 (answered by ikleyn)

Can I please have your assistance? Solve the system: 2x + y = 5
                          (answered by josgarithmetic)

Solve the system.
x-y+z=0
x+y+z=-2... (answered by Alan3354,ikleyn)

Solve the system:

5x - 3y + z = -6
x + 3y - z = 0
4x + y + z =... (answered by checkley71)