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Linear Algebra Help?

  1. Jun 18, 2013 #1
    1. The problem statement, all variables and given/known data
    Find a system of two equations in two variables, x and y, that has the solution set given by the parametric representation x=t and y=3t-4, where t is any real number.


    2. Relevant equations
    x=t and y=3t-4, where t is any real number


    3. The attempt at a solution
    y=3x-4 which means that x=(y+4)*1/3. But that is still only one equation and I can't figure out what the other one is. If there are two equations with two unknowns, couldn't the solutions be precise numbers? Since the solution given is parametric, I think there is only one equation in two variables. However, this does not satisfy the question's requirements. What is going on?
     
  2. jcsd
  3. Jun 18, 2013 #2

    Dick

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    I agree with you. It's probably just a mistake in the problem. If you want a second equation you could always suggest something like x=x or something else redundant. But that's pretty pointless.
     
  4. Jun 18, 2013 #3
    OK thanks for confirming my thought.
     
  5. Jun 19, 2013 #4

    HallsofIvy

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    Two independent equations in x and y will necessarily have a unique solution, not an infinite set of equations as you are given. Yes, x and y must satisfy y= 3x- 4 which I would write as 3x- y= 4. A second equation must be a multiple of that, say, 9x- 3y= 12.
     
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