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Need help with basic system of equations with two unknown values

  1. May 22, 2013 #1
    1. The problem statement, all variables and given/known data

    This is the problem:

    |4(x+2) - 7(x-y) = 7
    |7(x+y) + 10(x-2) = 79

    I need to solve this, I'm not quite sure what to do, the operators in the brackets are different, so even if I multiply by -1, if the operator in front of one variable changes, the other one will change too, still making them incompatible with the bottom one.

    2. Relevant equations

    3. The attempt at a solution

    I tried going the straight way by just doing all the operations until I get them to a simple as possible state:

    |4(x+2) - 7(x-y) = 7
    |7(x+y) + 10(x-2) = 79


    |4x + 7y + 1 = 0
    |10x + 7y -99 = 0

    This however doesn't get me anywhere.Could someone offer some help?(I know the problem sounds way too stupid :( )
    Combining them gives me:

    14x+ 14y - 98 = 0 ,which I turn into:
    x + y - 7 = 0 , which still doesn't really get me anywhere, x + y = 7.The book says the answer is 5 and 2, but not sure how to solve it properly.
  2. jcsd
  3. May 22, 2013 #2


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    Staff Emeritus
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    Homework Helper

    Why don't you expand out the brackets and collect like terms?
    For instance:
    4(x+2) - 7(x-y) = 7 turns into 4x + 8 - 7x - 7y = 7 turns into -3x - 7y = -1
  4. May 22, 2013 #3
    I think I solved it, is this correct:

    I expanded the brackets as you said, but multiplied the bottom one with (-1), so I got this:

    4x + 8 - 7x + 7y = 7
    -7x - 7y - 10x +20 = -79

    Then I collect them, so 7y and (-7y) are removed, leaving only X.
  5. May 23, 2013 #4


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    I'm not sure you understand: You have two simultaneous equations with unknowns x and y. You are supposed to determine the values of x and y which satisfy the equations.
  6. May 23, 2013 #5
    Yeah when only x is left I find it, then replaced it with the found value in the top formula to find y.
  7. May 23, 2013 #6


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    Staff: Mentor

    If I understand what is going on you are trying to add both equations side by side in such a way one of the unknowns cancels out. That's an OK method, but you can also use different approach - solve one of the equations for one unknown, and plug it into the other equation:


    From the first equation


    plugging into the second


    collecting like terms




    and you have an equation in one unknown only (actually it got solved just by tidying it up).

    And most likely you misunrderstood what SteamKing meant by "collect like terms" - he meant to combine together all expressions containing each unknown, and all free expressions. To quote his post again:

    4x + 8 - 7x - 7y = 7

    after grouping:

    (4x - 7x) - 7y = (7 - 8)

    and this directly yields

    -3x - 7y = -1
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