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Thread: system of equations problem

  1. September 20th 2009, 08:25 PM #1
    quah13579
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    Question system of equations problem

    Solve the following system of equations.

    <br /> x_1-x_2+x_3=-5<br />
    <br /> 3x_1+x_2-x_3=25<br />
    <br /> 2x_1+x_2+3x_3=20<br />
    <br /> 6x_1+x_2+3x_3=40<br />

    Does this system has a unique solution or infinitely many solutions? Justify your answer.

    please explain to me how to do it, thank you!
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  2. September 20th 2009, 09:26 PM #2
    Bruno J.
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    This is a very standard problem. Do you have a textbook? It should have examples...
    I'd be surprised if you were asked to solve this without first being given the proper tools.
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  3. September 20th 2009, 10:03 PM #3
    Prove It
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    Quote Originally Posted by Bruno J. View Post
    This is a very standard problem. Do you have a textbook? It should have examples...
    I'd be surprised if you were asked to solve this without first being given the proper tools.
    It doesn't look so standard to me... four equations in three unknowns...
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  4. September 20th 2009, 10:30 PM #4
    quah13579
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    Quote Originally Posted by Bruno J. View Post
    This is a very standard problem. Do you have a textbook? It should have examples...
    I'd be surprised if you were asked to solve this without first being given the proper tools.
    we've already studied for 3 equations, not 4
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  5. September 20th 2009, 11:51 PM #5
    mr fantastic
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    Quote Originally Posted by quah13579 View Post
    Solve the following system of equations.

    <br /> x_1-x_2+x_3=-5<br />
    <br /> 3x_1+x_2-x_3=25<br />
    <br /> 2x_1+x_2+3x_3=20<br />
    <br /> 6x_1+x_2+3x_3=40<br />

    Does this system has a unique solution or infinitely many solutions? Justify your answer.

    please explain to me how to do it, thank you!
    Solve for x_1 by adding equations (1) and (2).

    Solve for x_1 by subtracting equation (3) from equation (4).

    What do you conclude?
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  6. September 21st 2009, 12:26 AM #6
    quah13579
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    Quote Originally Posted by mr fantastic View Post
    Solve for x_1 by adding equations (1) and (2).

    Solve for x_1 by subtracting equation (3) from equation (4).

    What do you conclude?
    I got x_1 = 5. so it is a unique solution right?
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  7. September 21st 2009, 06:36 PM #7
    mpl06c
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    it should be unique
    since there are more equations then unknowns, correct?
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  8. September 21st 2009, 06:46 PM #8
    mr fantastic
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    Quote Originally Posted by mpl06c View Post
    it should be unique
    since there are more equations then unknowns, correct?
    Incorrect.

    In the case of the question posted, there is a unique solution. However, when there are more equations then unknowns it is still possible for equations to be:

    1. Inconsistent (in which case there is no solution). eg. x + y = 3, 2x + 2y = -1, x - y = 2 (three equations, two unknowns, no solution)

    2. Redundant (in which case there may be infinite solutions). eg. x + y = 3, 2x + 2y = 6, -x - y = -3 (three equations, two unknowns, infinite solutions).
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  9. September 21st 2009, 07:05 PM #9
    mpl06c
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    oh ok... so in order to tell if it was uniqiue one would have to do RREF, correct?
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