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-   -   Finding intersections in graphs (https://www.askmehelpdesk.com/showthread.php?t=358484)

  • May 27, 2009, 01:03 PM
    leonardthegreat
    finding intersections in graphs
    how do you find intersections in two equations such as x^2/4+y^2=1 and x+y=1
  • May 27, 2009, 02:45 PM
    Perito

    The intersection is where the two lines/curves meet. If you graph them, there will be an intersection, and you can read it from the graph. Otherwise, you do something like this (I'll solve this using "substitution". There are other methods):



    therefore






    So, substituting 1-x for y, you get



    Simplifying and collecting terms







    factor



    x=0 and x=8/5 are the roots (solutions) of the equation. You can find the corresponding y values by substituting into the equations. If x=0 then y=1; if x=8/5 then y=-3/5. The two points of intersection are, therefore (0,1) and (8/5, -3/5)

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