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How to solve a double incognite equation?

  1. Oct 21, 2008 #1
    Hello! Im new here! And i really like this site! So heres is my problem:

    Well i know how to solve a simple equation with 2 incognites like:

    x+y=2

    x+4=2y

    So in this case i do a substitue y=x-2 and use it in the second equation and it would be like:

    x+4=2(x-2)

    But the problem is if they only give me one equation with 2 incognites how can i solve it?

    Example:

    3x-4y+2=2(x+1)


    Thanks!
     
  2. jcsd
  3. Oct 21, 2008 #2

    statdad

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    Homework Helper

    If all you are given is one equation in two unknowns - like your example

    3x-4y+2=2(x+1)

    and no other information, then you have only two choices

    1. Solve for x in terms of y: x = material involving only y and constants

    2. Solve for y in terms of x: y = material involving only x and constants

    Typically version 2 is selected, as we are accustomed to seeing equations with y isolated.
    What is the setting for this question?
     
  4. Oct 21, 2008 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    A single equation in two unknown numbers, x and y, has an infinite number of (x,y) solutions: The graph of something like 3x-4y+2=2(x+1) on an xy- coordinate system would be a straight line. Every point on the line gives an (x,y) pair that satifies the equation.
     
  5. Oct 21, 2008 #4
    So that means that x or y cant have an exact number because it can be any number, like it cant be x=2, it must be like x € (-infinite,infinite) like the inequations is that what you mean?
     
  6. Oct 21, 2008 #5

    HallsofIvy

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    Either x or y can be any number. Once one of them is chosen, the other is fixed.
     
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