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Math Help - Simultaneous equations

  1. #1
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    Simultaneous equations

    I have:

    2x-y+3z = 4
    x+y+az = 3
    x+ay+z = 3

    and I'm wondering what the easiest way to solve out a is, cause i've been trying and it just ends up looking worse than it did before i started out.. ^^
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by weasley74 View Post
    I have:

    2x-y+3z = 4
    x+y+az = 3
    x+ay+z = 3

    and I'm wondering what the easiest way to solve out a is, cause i've been trying and it just ends up looking worse than it did before i started out.. ^^
    What are you trying to find? if a=0 or a=1 the system is degenerate (reduces
    to two independent equations) and so has multiple solutions, any other
    value of a will allow a unique solution for x, y and z in terms of a.

    RonL
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    What are you trying to find? if a=0 or a=1 the system is degenerate (reduces
    to two independent equations) and so has multiple solutions, any other
    value of a will allow a unique solution for x, y and z in terms of a.

    RonL
    I think the system will have no solution for a = 0 ......

    2x - y + 3z = 4 ..... (1)
    x + y = 3 .... (2)
    x + z = 3 ..... (3)

    (1) + (2): 3x + 3z = 7 => x + z = 7/3 is inconsistent with (3).
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by mr fantastic View Post
    I think the system will have no solution for a = 0 ......

    2x - y + 3z = 4 ..... (1)
    x + y = 3 .... (2)
    x + z = 3 ..... (3)

    (1) + (2): 3x + 3z = 7 => x + z = 7/3 is inconsistent with (3).
    Yup, made a mistake when examining that case

    RonL
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