Question 111134
Hello

Solving for 3 variables is similar to solving for 2 variables except that you have to reduce these to 2 equations with 2 similar variables.

Given X + Y + 2Z =5 -----------(1)
X + Y =5 -------------------(2)
X + 3Y + Z =11 ----------------(3)

(3) * 2 gives 2X + 6Y + 2Z = 22 --------------(4)

               X + Y + 2Z = 5 ----------------(1)

Subtracting (1) from (4) gives, 
  X + 5Y = 17 ---------------(5)
  X + Y = 5 ---------------(2)

Subtracting (2) from (5) gives, 4Y = 12
                                Y = 12/ 4
                                Y = 3


Plugging this value of Y in (2),
X + 3 = 5
==> X = 5 - 3
==> X = 2

Substituting these values in (3) gives,
2 + 3(3) + Z = 11
==> 2 + 9 + Z = 11
==> 11 + Z = 11
==> Z = 11 - 11
==> Z = 0

Thus X = 2;   Y = 3;   Z = 0 


Best of Luck!!!