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Math Help - Systems in 3 variables #2

  1. #1
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    Systems in 3 variables #2

    Have to find x,y,and z.

    1.)
    x - y - 5z = -2
    y + 3z = 9
    x + y + z = 16

    HELP ASAP please& thank you
    Last edited by mr fantastic; December 2nd 2009 at 09:01 PM. Reason: Changed post title
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  2. #2
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    Hello, kelsikels!

    1) Solve: . \begin{array}{ccc} <br />
x - y - 5z &=& \text{-}2 \\ \qquad y + 3z &=& 9 \\ x + y + z &=& 16 \end{array}
    There is an infinite number of solutions:

    . . \begin{Bmatrix}x &=& 7 + 2t \\ y &=& 9 - 3t \\ z &=& t \end{Bmatrix}

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  3. #3
    MHF Contributor

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    kelsikels, you should have at least tried yourself! For example, if you add the first and second equations, the "y" and "-y" cancel leaving you an equation in only x and z. If you add the first and third equations, again "y" and "-y", giving a second equation in only x and y. If those are "independent" (neither equation is just a multiple of the other) you can solve those two equations for x and z, then go back and solve for y. If they are not, as Soroban implies, you can solve for, say, x, in terms of z and then solve for y in terms of z. That gives a different solution for each value of z.
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