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  1. #1
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    math help

    solve by addition method indicate whether it is independent, inconsistent or depnedent,


    x+3(y-1)=11
    2(x-y+8y=28
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by fancyface View Post
    solve by addition method indicate whether it is independent, inconsistent or depnedent,


    x+3(y-1)=11
    2(x-y+8y=28
    Need a little help with that last equation. You're missing a ")."

    -Dan
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  3. #3
    Forum Admin topsquark's Avatar
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    From a PM from fancyface:

    This is the message:
    x+3(y-1)=11
    2(x-y)+8y=28

    -Dan
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by topsquark View Post
    From a PM from fancyface:

    This is the message:
    x+3(y-1)=11
    2(x-y)+8y=28

    -Dan
    I'm going to simplify these equations a touch:
    x + 3y = 14
    2x + 6y = 28

    Note that if we multiply the top equation by 2 we get:
    2x + 6y = 28
    which is just the same as the second equation.

    This means we have an infinite number of solutions to x and y, all lying on the line y = -\frac{1}{3}x + \frac{14}{3}. You'd have to look up the definitions of dependent and independent. But I can say that the system is NOT inconsistent since we have at least one solution.

    -Dan
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  5. #5
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    Quote Originally Posted by topsquark View Post
    I'm going to simplify these equations a touch:
    x + 3y = 14
    2x + 6y = 28

    Note that if we multiply the top equation by 2 we get:
    2x + 6y = 28
    which is just the same as the second equation.

    This means we have an infinite number of solutions to x and y, all lying on the line y = -\frac{1}{3}x + \frac{14}{3}. You'd have to look up the definitions of dependent and independent. But I can say that the system is NOT inconsistent since we have at least one solution.

    -Dan
    x = 14
    y = 0

    Note the gausselim (echelon form) is x + 3y = 14 // -5y = 0;

    I agree with topsquark when he says that the system is not inconsistent (and thus consistent), since we have at least one solution. In fact, we have exactly one solution. Setting up the matrix of coefficients for the above and then augmenting it, we can clearly see when row reducing it that there are no pivots in the augmented column, thus it is consistent. Further, we know it is linearly INDEPENDENT since there are no free variables and the columns span R^2.
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by AfterShock View Post
    In fact, we have exactly one solution.
    As I mentioned previously we have an infinite number of solutions. All points on the line y = -\frac{1}{3}x + \frac{14}{3} will work.

    -Dan
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  7. #7
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    Quote Originally Posted by topsquark View Post
    As I mentioned previously we have an infinite number of solutions. All points on the line y = -\frac{1}{3}x + \frac{14}{3} will work.

    -Dan
    Indeed, I believe I was looking at the homogeneous system.
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