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Graphing system of equations

  1. Feb 25, 2007 #1
    1. The problem statement, all variables and given/known data

    Solve the system of equations graphically.

    2. Relevant equations

    1)
    4x - y = 5
    y = 4 - 5x^2


    2)
    2x^2 + y^2 = 33
    x^2 - y^2 = 12

    3. The attempt at a solution

    The answers I got for the intersecting points are:
    1)
    (1, -1)

    And

    2)
    (+/- 3.7, +/- 1.8)

    These are estimates from graphing, but I'm not sure if I'm close... I don't know how to check myself algebraically yet... =/
     
  2. jcsd
  3. Feb 25, 2007 #2

    robphy

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    You should be able to at least substitute your graphically-obtained points into the equations.
     
  4. Feb 25, 2007 #3
    I did that mostly...

    but for the equations like y = 4 - 5x^2, is that the same as saying:

    y = 4 - 5(-1)^2?
    or would it bet
    y = 4 - 5(-1^2)?

    for that particular equations here are my points:

    x............| y
    0 .............4
    +/-.89 ......0
    +/- 1 ......-1
    +/- 2 ......-3
     
  5. Feb 25, 2007 #4

    Integral

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    for your first problem you have found a possible solution at (1,-1).

    Your equations are:
    y= 4x -5
    and
    y= 4 - 5 x 2

    Plugging x = 1 into each of these yields:

    y = 4(1) -5 = -1

    Thus your point is a solution for this equation.

    Repeat for the second equation.

    y = 4 - 5(-1) 2 = 4 -5 = -1

    Thus your solution works in both equations and is an intersection point.

    Do the same thing with your second problem.
     
  6. Feb 25, 2007 #5
    groovy, good to know i'm on the right path...

    could you show me how to solve algebraically (#1)? If you could give me a start I'll work on it and let you know where I get....
     
  7. Feb 26, 2007 #6

    Integral

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    In my last post I expressed both equatons of your first problem as y expressed in terms of x. Eliminate y by setting them equal, then solve for x.

    y= 4x -5
    y = 4 - 5x 2
    4x -5 = 4 - 5x 2
    5x 2 + 4x - 9 = 0

    Can you finish?
     
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