Which equations can pair with y = 3x – 2 to create a consistent and independent system? x = 3y – 2 y = –3x – 2 y = 3x + 2 6x – 2y = 4 3y – x

Question

Which equations can pair with y = 3x – 2 to create a consistent and independent system? x = 3y – 2 y = –3x – 2 y = 3x + 2 6x – 2y = 4 3y – x = –2

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Hải Đăng 1 year 2021-09-03T17:00:02+00:00 1 Answers 103 views 0

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    2021-09-03T17:01:45+00:00

    Answer:

    [tex](a)\ x = 3y – 2[/tex]

    [tex](b)\ y = -3x – 2[/tex]

    [tex](e)\ 3y – x = -2[/tex]

    Step-by-step explanation:

    Given

    [tex]y =3x -2[/tex]

    Required

    Equations that can create consistent and independent systems

    For a pair of equation to have consistent and independent systems, the equations must have different slopes.

    An equation of the form [tex]y = mx + c[/tex] has m has its slope.

    In [tex]y =3x -2[/tex]

    [tex]m = 3[/tex] — slope

    Considering the options

    [tex](a)\ x = 3y – 2[/tex]

    Make y the subject

    [tex]x = 3y – 2[/tex]

    [tex]3y = x+2[/tex]

    Divide by 3

    [tex]y = \frac{1}{3}x+\frac{2}{3}[/tex]

    The slope is:

    [tex]m_1 = \frac{1}{3}[/tex]

    Hence, (a) can make a consistent and independent system with [tex]y =3x -2[/tex]

    [tex](b)\ y = -3x – 2[/tex]

    The slope is:

    [tex]m= -3[/tex]

    Hence, (b) can make a consistent and independent system with [tex]y =3x -2[/tex]

    [tex](c)\ y = 3x + 2[/tex]

    The slope is:

    [tex]m=3[/tex]

    Hence, (c) cannot make a consistent and independent system with [tex]y =3x -2[/tex]

    [tex](d)\ 6x – 2y = 4[/tex]

    Make y the subject

    [tex]2y = 6x -4[/tex]

    Divide by 2

    [tex]y = 3x -2[/tex]

    The slope is

    [tex]m =3[/tex]

    Hence, (d) cannot make a consistent and independent system with [tex]y =3x -2[/tex]

    [tex](e)\ 3y – x = -2[/tex]

    Make y the subject

    [tex]3y = x -2[/tex]

    Divide by 3

    [tex]y = \frac{1}{3}x -\frac{2}{3}[/tex]

    The slope is:

    [tex]m = \frac{1}{3}[/tex]

    Hence, (e) can make a consistent and independent system with [tex]y =3x -2[/tex]

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )