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Math Help - Does this have one solution or inifinte

  1. #1
    Senior Member
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    Does this have one solution or inifinte

    x − 3y + z = 1
    x + y + 2z = 14

    1 -3 1 | 1
    1 1 2 | 14

    1 -3 1 | 1
    0 4 1 | 13

    1 -3 1 | 1
    0 1 1/4 | 13/4

    1 0 7/4 | 43/4
    0 1 1/4 | 13/4

    So x = 43/4 y = 13/4 and z = 0. Which is one solution.

    But because there is 1 variable in my last reuction does this mean there are infinite solutions?
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  2. #2
    MHF Contributor Amer's Avatar
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    it has infinite numbers of solutions, for any value of z u have different values of x,y
    it is clear from the beginning since u have three variables and two equations
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  3. #3
    Senior Member yeKciM's Avatar
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    you can do it so that for "z" there is different type of solutions

     x-3y= 1-z

     x+y = 14-2z

    than depending on your determinants  D, D_x, D_y you discuss what can be and how many solutions
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