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One solution, no solution or infinite solutions with k

  1. May 1, 2016 #1
    1. The problem statement, all variables and given/known data
    ¿which one values of "k" the next equation sistem dont have solutions, exactly one solution, infinite solutions?
    2. Relevant equations
    testy.png

    3. The attempt at a solution
    well i guess i need to assign values to test the equations, but i am asking for a metod to help solve this if they are more complex, by the way i am finding solutions, like k=6
    but i dont know if foward in number scale are there other solutions
     
  2. jcsd
  3. May 1, 2016 #2

    SammyS

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    In general, how do you solve such a system for x and y ?
     
  4. May 1, 2016 #3
    well doing matrix, or for this simple equations sustitution metod, but how to solve whith a teorical k in place?
     
  5. May 1, 2016 #4

    SammyS

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    Leave it as k. Try substitution.
    Just keep k and solve as you would normally solve with substitution.
     
  6. May 1, 2016 #5
    do you mean, solve like k doesnt exist? and put a 0?
     
  7. May 1, 2016 #6

    SammyS

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    No leave it as k.
    Use algebra.
     
  8. May 1, 2016 #7
    its says k=6 so i am ok, but its ok to do the metod whith complex equations? like 5x5
     
  9. May 1, 2016 #8

    SammyS

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    Now put 6 in for k. Solve the system again in this specific case. (Matrix method may be clearer.)

    (I don't understand your last question.)
     
  10. May 1, 2016 #9
    there are some exercices when they put 3x3 equation sistem and in all the equations a k, or in two of them and they ask the same about solutions
     
  11. May 1, 2016 #10

    SammyS

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    If you use a 6 for k, how would you describe the solution set?
     
  12. May 1, 2016 #11
    correct me if i am wrong but must be k=6 and must be x>y because x-y=positive number, so y=x-3
     
  13. May 1, 2016 #12

    SammyS

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    k must be 6 , that's correct.

    y does not have to be positive.

    It is also correct that y = x - 3.

    How do you describe the equation y = x - 3 ?

    How many possible solutions does that give for (x,y) ?
     
  14. May 1, 2016 #13

    epenguin

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    Maybe it's unfair to call this 'obvious'. Maybe it's obviousness depends on familiarity.

    But if it doesn't hit you in the eye now, after you divide the second equation by 2 doesn't it?
     
  15. May 1, 2016 #14
    I think its a linear function, starts at - 3 in y axis, and the solutions for that only and specific equation must be infinite
     
  16. May 1, 2016 #15
    Yes this is easy, i am looking for a metod to do this right and quick for more complex equation system, for my test
     
  17. May 1, 2016 #16

    SammyS

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    (Please try to use the "Reply" feature, so it's clear who you are addressing and what question you are answering.)

    The y-intercept is -3, but the line doesn't start there.
     
  18. May 1, 2016 #17

    Mark44

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    The system is
    $$x - y = 3$$
    $$2x - 2y = k$$
    It might be helpful to look at the geometry here. If k = 6, the two equations are equivalent -- they describe exactly the same line. Any point (x, y) on one line is also on the other line.

    If ##k \ne 6##, what can you say about the lines? Do they intersect?

    Is it possible for the two lines to intersect at exactly one point?
     
    Last edited: May 2, 2016
  19. May 1, 2016 #18
    interesting, the way of the geometry, well if k its not 6 then the lines will be parallel whiout any intersection, am i right?
     
  20. May 1, 2016 #19

    SammyS

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    Right !
     
  21. May 1, 2016 #20
    thanks for your time, people it was very rich the explanation and hit direct into the point of my question, thanks really
     
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