2 equations, 2 unknowns

  1. 1. The problem statement, all variables and given/known data

    I can't remember how to solve these equations like this one. I need to solve for each variable. I'm not sure I've ever known how to do this.

    -720 + Tab*cos(36.8699) + Taf*cos(20.556)

    660 + Tab*sin(53.1301) + Taf*sin(69.444)

    I need to solve for both Tab and Taf. This is possible, right?

    2. Relevant equations



    3. The attempt at a solution

    Don't even know where to start...need help!
    Thanks,
    Brad
     
  2. jcsd
  3. These are not equations, there are no equal signs. Thus they cannot be solved. But, if they were to have equal signs, sin (53.1301) just represents a number right? If you 53.1301 is in degrees and not radians (very likely) then sin (53.1301)= [tex]0.8[/tex]

    To solve two equations in two unkowns, there are a few ways. Perhaps the easiest is to solve for one variable in one of the equations in terms of the other equation and then plug that into the other equation.


    So lets say you have two equations in y and x such as:

    3x+y=5
    y+5x=2

    You could solve the second one for y.. y=2-5x right?

    now plugging it into the first one you get
    3x+2-5x=5

    -2x=3
    x=-2/3

    Now just plug x=-2/3 into the other equation and solve for y. Easy.
     
  4. Ok so is this right then....

    Solving second equation for Tab

    Tab = =(-Taf(.936) - 660)/.8

    Then insert back into equation 1....

    -720 - Taf(.936) - 660 + Taf(.936) = 0

    These are all equal to zero, forgot to add that in....and yes, they are degrees.

    If that is right, I can't get an answer to come out.
     
  5. cristo

    cristo 8,412
    Staff Emeritus
    Science Advisor

    Check your signs. The second equation gives Tab*sin(53.1301) =- Taf*sin(69.444)-660. Plug this into the first and you get {Taf/sin(53.1..)}*[-sin(69.444)-660]*cos(36.8699) + Taf*cos(20.556)=720.

    I suspect you are missing a minus sign.
     
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