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6 January, 23:49

The sum of two numbers is 65. The difference of the two numbers is 27. Write and solve a system of linear equations to find the two numbers. Let x represent the greater number, and let y represent the lesser number.

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  1. 7 January, 01:31
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    X + y = 65 The sum of two numbers (x and y) is 65

    x - y = 27 The difference of the two numbers is 27

    This can easily be solved with elimination.

    2x = 92

    x = 46

    Then we solve for y replacing the x value for x.

    46 + y = 65

    y = 19

    The solution is (46, 19).

    If you want substitution:

    x + y = 65

    x - y = 27

    y = 65 - x

    x - y = 27

    x - (65 - x) = 27

    x - 65 + x = 27

    2x - 65 = 27

    2x = 92

    x = 46

    Then solve for y using either equation.

    46 - y = 27

    - y = - 19

    y = 19

    We get the same solution (46, 19). You can check this by plugging in the x and y values into one or both equations.
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