9514 1404 393
Answer:
 (-2, 5, 7)
Step-by-step explanation:
The problem statement lets us write three equations for the three numbers x, y, and z.
 x + y + z = 10
 -x + 2y = 12
 x - y + 2z = 7
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Adding the second equation to each of the other two gives ...
 3y +z = 22
 y +2z = 19
Subtracting the second of these from double the first gives ...
 2(3y +z) -(y +2z) = 2(22) -(17)
 6y +2z -y -2z = 44 -19
 5y = 25
 y = 5
 z = 22 -3(5) = 7 . . . . . . from 3y+z=22
 x = 10 -5 -7 = -2 . . . . . .from x+y+z=10
The numbers are (x, y, z) = (-2, 5, 7).
