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

Distract equation (2) from equation (1) (both sides). You ill get

2y = 6-2 = 4  --->  y = 2.

Substitute y = 2 into equations (1) and (3). You will get

 x + z =  4,        (4)    ( from (1) )
2x - z = -1.        (5)    ( from (3) )

Add equations (4) and (5). You will get

3x = 3  --->  x = 1.

Now everybody can determine z. From (4), z = 4 - x = 4 - 1 = 3.

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

x + y + z = 6 -------- Considering X is same as x ------- eq (i)

x - y + z = 2 -------- Considering X is same as x ------- eq (ii)

2x + y - z = 1 ------- eq (iii)

2y = 4 ------ Subtracting eq (ii) from eq (i)

y = , or 2



3x = 3 ------ Adding eqs (ii) & (iii)

x = , or 1



1 + 2 + z = 6 ------- Substituting 1 for x, and 2 for y in eq (i)

3 + z = 6

z = 6 - 3, or 3

Solution set:  

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