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The sum of twice a number and another number is 24. The difference of twice the first number and the other number is 12. Which system would model this situation, and what is the solution?

  • Math -

    x = 1st number and y = second number

    2x + y = 24
    2x - y = 12

    Can you finish from here? Add the two equations to eliminate y and solve for x.

    Then find y.

    Be sure to check both x and y in both equations to be sure you are correct.

  • Math -

    2 x + y = 24
    y - 2x = 12

    4 x = 12
    x = 3

    y = 24 - 6 = 18

    6 + 18 = 24 yes
    18 - 6 = 12 yes

    note you could have written
    2 x + y = 24
    2 x - y = 12

    2 y = 12
    y = 6

    2x + 6 = 24
    x = 9

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