# 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

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations -> 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       Log On

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 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!!!