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    3x-7y=3
    2x+2y+5z=2
    x+3y+4z=1

    given that there were no unique solutions to these equations,I manipulated them to get

    4y-3z=0
    and
    4y+3z=0

    I'm confused whether these are consistent or inconsistent, and how to geometrically interpret the three planes ?

    any help would be great!
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    (Original post by F3rnw3h)
    3x-7y=3
    2x+2y+5z=2
    x+3y+4z=1

    given that there were no unique solutions to these equations,I manipulated them to get

    4y-3z=0
    and
    4y+3z=0

    I'm confused whether these are consistent or inconsistent, and how to geometrically interpret the three planes ?

    any help would be great!
    Do

    4y-3z=0
    and
    4y+3z=0

    have a solution?


    Two equations are inconsistent when you have 4x+3y =1, and 4x+3y=6, for example. The "4x+3y" has to simultaneously have two values - which isn't possible, and then they are inconsistent.

    Edit: I don't know how you arrived at that point, but suspect you've made an error further back, but depends on what you think the final solution is.
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    (Original post by F3rnw3h)
    3x-7y=3
    2x+2y+5z=2
    x+3y+4z=1

    given that there were no unique solutions to these equations,I manipulated them to get

    4y-3z=0
    and
    4y+3z=0

    I'm confused whether these are consistent or inconsistent, and how to geometrically interpret the three planes ?

    any help would be great!
    pretty sure you've made an error somewhere, can you show your working?
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    (Original post by ghostwalker)
    Do

    4y-3z=0
    and
    4y+3z=0

    have a solution?


    Two equations are inconsistent when you have 4x+3y =1, and 4x+3y=6, for example. The "4x+3y" has to simultaneously have two values - which isn't possible, and then they are inconsistent.

    Edit: I don't know how you arrived at that point, but suspect you've made an error further back, but depends on what you think the final solution is.
    Thankyou! I'd made a sign error somewhere. But now I know that the equations are consistent, how do I know whether the planes form a sheaf or all the planes coincide?
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    (Original post by _gcx)
    pretty sure you've made an error somewhere, can you show your working?
    You're right, I made a sign error -thanks!
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    (Original post by F3rnw3h)
    Thankyou! I'd made a sign error somewhere. But now I know that the equations are consistent, how do I know whether the planes form a sheaf or all the planes coincide?
    have you found a finite or infinite set of solutions? also, you know that the planes are distinct and hence don't "coincide".
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    (Original post by _gcx)
    have you found a finite or infinite set of solutions? also, you know that the planes are distinct and hence don't "coincide".
    Thanks! Would you have an example of what a set of coinciding planes look like?
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    (Original post by F3rnw3h)
    Thanks! Would you have an example of what a set of coinciding planes look like?
    a simple one would be x+y+z = 1, 2x+2y+2z = 2, 3x+3y+3z=3.
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    (Original post by _gcx)
    a simple one would be x+y+z = 1, 2x+2y+2z = 2, 3x+3y+3z=3.
    Thankyou! Makes more sense now
 
 
 
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