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How many pairs of integers (x,y) satisfy the conditions y=3x-1,6x-2y=2 and 0<=x<=25?

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    6 x - 2 y = 2 Subtract 6 x to both sides

    6 x - 2 y - 6 x = 2 - 6 x

    - 2 y = 2 - 6 x Divide both sides by - 2

    - 2 y / - 2 = 2 / - 2 - 6 x / - 2

    y = - 1 + 3 x

    y = 3 x - 1


    Equations :

    y = 3 x - 1 and 6 x - 2 y = 2 are same equation.


    On interval 0 < = x < = 25 you have 26 integers :

    0 = first integer

    1 = second integer

    2 = third integer

    ...

    25 = twenty-sixth integer

    You have 26 pairs of integers ( x , y ) which satisfied given conditions.

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