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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

    into:

    |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

    SteamKing

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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

    SteamKing

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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

    Borek

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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:

    x+y=1
    2x+y=3

    From the first equation

    y=1-x

    plugging into the second

    2x+1-x=3

    collecting like terms

    (2x-x)=3-2

    or

    x=1

    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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