SOLUTION: Please help me solve for x, y, z. I understand how to solve for two variables but I don't understand how to solve for three. Solve for x, y, and z. X + Y + 2Z =5 X + Y =5

Question 111134: Please help me solve for x, y, z. I understand how to solve for two variables but I don't understand how to solve for three.
Solve for x, y, and z.
X + Y + 2Z =5
X + Y =5
X + 3Y + Z =11

Answer by dolly(163) (Show Source): You can put this solution on YOUR website!
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!!!
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