SOLUTION: Find three numbers such that: their sum is 12;the sum of the first, twice the second, and three times the third is 31;the sum of the third and nine times the second is 1.

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Question 1053040: Find three numbers such that: their sum is 12;the sum of the first, twice the second, and three times the third is 31;the sum of the third and nine times the second is 1.
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
x + y + z = 12
x + 2y + 3z = 31
9y + z = 1 ----> z = 1 - 9y

Substitute the expression for z into the first two equations.

x + y + (1 - 9y) = 12 ---> x - 8y = 11
x + 2y + 3(1 - 9y) = 31 ---> x - 25y = 28

Subtract the equations to get

x - 8y = 11
-x + 25y = -28
----------------------
17y = -17
y = -1

9y + z = 1
9(-1) + z = 1 ---> z = 10

x + (-1) + 10 = 12
x = 3

solution: (x, y, z) = (3, -1, 10)