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Math Help - infinite solutions

  1. #1
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    infinite solutions

    Hello, we have been solving linear equations in three variables and one of them has the final two equations as:

    -x-3z=-1
    x+3z=1

    which will answer as an infinite number of solutions possible.

    My question is, is it acceptable to simply write "infinite number of solutions possible" in an exam, or should I express that some other way ?

    Thanks for any help.
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  2. #2
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    Yes. You can add that this is because the two equations are identical (what happens when you multiply both sides of the first equation by -1?)
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  3. #3
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    If you wanted to really impress (and/or shock) your teacher, you could find a general expression for all of those "infinite" number of solutions. Of course, that would depend upon what the first equation was.

    If the problem was, say, x+ y+ z= 1, -x-3z=-1, x+3z=1, you could rewrite the last equation as x= 1- 3z and put that into the first equation to get 1- 3z+ y+ z= 1+ y- 2z= 1 so that y= 2z. Now you can write that (x, y, z)= (1- 3z, 2z, z) is a solution for z any number
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