a pair of straight line

y=3x

y= -x

then -3x^2-2xy+y^2=0 represent the above two lines,why???

why multiply both equation and state that it is a representation of two straight line??

thz

1 個解答

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  • 1 十年前
    最愛解答

    -3x^2-2xy+y^2=0 represent the above two lines

    This sentense means -3x^2-2xy+y^2=0 can represent all the points in y = 3x and y = -x.

    We have two equations :

    y = 3x ------ 1

    y = -x ------ 2

    We aim to find an equation to represent the two equations above :

    y - 3x = 0

    y + x = 0

    Multiplying two equations

    (y - 3x)(y + x) = 0

    thus we get -3x^2 -3xy + xy + y^2 = 0

    finally : -3x^2-2xy+y^2=0

    Thus -3x^2-2xy+y^2=0 represent the above two lines.

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