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14 November, 18:37

If a = - 12/5, then 5x + 2y = 6 and 3x - ay = 4 are parallel.

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  1. 14 November, 19:21
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    5x + 2y = 6

    Add - 2y to both sides

    5x = - 2y + 6

    Divide both sides by 5

    x = - 2 / 5 y + 6/5

    that into the second equation:

    3 ( - 2 / 5 y + 6/5 ) + 12/5 y = 4

    simplify

    6/5 y + 18/5 = 4

    Add (-18) / 5 to both sides

    6/5 y = 2 / 5

    divide both sides by 6/5

    y = 1/3

    substitute 1/3 for y in x = - 2/5y + 6/5 to solve for x

    x = - 2/5 (1/3) + 6/5

    x = 16/15

    so x = 16/15 and y = 1/3

    now replace both x and Y in each of the original equations to check the answers:

    5 (16/15) + 2 (1/3) = 5 1/3 + 2/3 = 6 true

    3 (16/15) - - 12/5 (1/3) = 4 true

    so they are parallel
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