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Math Help - Linear Equation

  1. #1
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    Linear Equation

    Definiton of a linear equation

    a_{1} x_{1} + a_{2}x_{2}... a_{n}x_{n} = b where b is a real number

    Note if b = 0, it's a homogeneous equation.

    What are some reasons why these statements are true?

    3x - 4xy = 0 - not linear

    x^{2} + y^{2} = 4 - not linear

    (\sin2x) - y = 14 linear
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  2. #2
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    Re: Linear Equation

    Quote Originally Posted by Jason76 View Post
    Definiton of a linear equation

    a_{1} x_{1} + a_{2}x_{2}... a_{n}x_{n} = b where b is a real number

    Note if b = 0, it's a homogeneous equation.

    What are some reasons why these statements are true?

    3x - 4xy = 0 - not linear
    the "xy" term cannot be written in the form "ax+ by" for any numbers a and b.

    x^{2} + y^{2} = 4 - not linear
    The terms x^2 and y^2 cannot be written in the form "ax+ by" for any numbers a and b.

    (\sin2x) - y = 14 linear
    sin(2x) cannot be written in the form "ax+ by" for any numbers a and b.
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