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Math Help - Graphing linear system

  1. #1
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    Graphing linear system

    I have to graph two linear systems and solve them geometrically. However, I am finding that one linear equation in the system contradicts another. Please note that those are two linear systems I have set up myself in the process of solving a 2x2 matrix game, so I'm not sure whether the linear systems I have arrived to themselves are right.

    System 1

    Objective function
    F = x + y = 1/v
    Constraints
    x, y ≥ 0
    1x + 7y ≥ 1
    11x + 2y ≥ 1

    Now, I first have to draw the boundaries of the constraints on the graph. I find some points of the boundaries and plot it. The boundaries are 1x + 7y = 1 and 11x + 2y = 1.
    If x = 2 ("2" is greater than zero)
    then 1(2) + 7y = 1, then y = -1/7
    and 11(2) + 2y = 1, then y = -10.5
    The results I get for "y" on the boundary are systematically negative, while the constraint x, y ≥ 0 require that both x and y are 0 or positive. I am confused. Is there something wrong with the linear systems themselves?
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  2. #2
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    Re: Graphing linear system

    The region of plane which comprises of solution has been marked. I am sure it will be of helpGraphing linear system-graph.png
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  3. #3
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    Re: Graphing linear system

    Thank you!!! It did help me a lot to solve the problem :] I've managed to solve it. Thanks again!
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