The sum of three numbers is 10. Two times the second number minus the first number is equal to 12. The first number minus the second number plus twice the third number equals 7. Find the numbers.

9514 1404 393

  (-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).

step-by-step explanation:

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