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Extras for Experts XYZ - Solve Systems of Equations

Solutions

  1. x = 5, \ y = 4, \ z = 6
  2. x = 5, \ y = 9, \ z = 6
  3. x = 7, \ y = 6, \ z = 9
  4. x = 8, \ y = 7, \ z = 6

Eric wrote these equations to represent pictures of scales with blocks. Figure out the value of each unknown.

1. \quad y + y +  z + z = 20 \qquad \quad x = \underline{\;\;\;\;\;\;\;\;\;\;}\!\\{\;} \quad \ x + x + y = 14 \qquad \quad \quad \ \ y = \underline{\;\;\;\;\;\;\;\;\;\;}\!\\{\;} \quad \ x + x + y + z = 20 \qquad \ \ \ z = \underline{\;\;\;\;\;\;\;\;\;\;}

2. \quad x + x + y + z = 25 \qquad \quad x = \underline{\;\;\;\;\;\;\;\;\;\;}\!\\{\;} \quad \ x + y + y = 23 \qquad \qquad \quad y = \underline{\;\;\;\;\;\;\;\;\;\;}\!\\{\;} \quad \ x + y + z = 20 \qquad \qquad \quad z = \underline{\;\;\;\;\;\;\;\;\;\;}

3. \quad x + y + z + z = 31 \qquad \quad \ x = \underline{\;\;\;\;\;\;\;\;\;\;}\!\\{\;} \quad \ x + y + z = 22 \qquad \qquad \quad y = \underline{\;\;\;\;\;\;\;\;\;\;}\!\\{\;} \quad \ x + z = 16 \qquad \qquad \qquad \ \ z = \underline{\;\;\;\;\;\;\;\;\;\;}

4. \quad x + y + z = 21 \qquad \qquad \quad x = \underline{\;\;\;\;\;\;\;\;\;\;}\!\\{\;} \quad \ x + x + y + z = 29 \qquad \quad \ y = \underline{\;\;\;\;\;\;\;\;\;\;}\!\\{\;} \quad \ y + y + z = 20 \qquad \qquad \quad z = \underline{\;\;\;\;\;\;\;\;\;\;}

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