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Math Help - help solve

  1. #1
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    help solve

    Use elimination to solve: x/3 + 4y = 30 and 2x - y = 5.

    I need help solving this problem. If it's not to much trouble can some one help my or give me an example to help me out. I greatly apprecite the help.
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  2. #2
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    Hi
    Use elimination to solve is a clue. It's just a fancy way of saying get rid of a variable (x or y) from one of the equations.

    x/3 + 4y = 30 and 2x - y= 5.

    Because the coefficients of y are nice I chose to get rid of it from one of the equations.
    This step is called rearranging the equation.
    2x -y =5
    2x=5+y
    2x-5=y

    So what next? Here is the elimination part. We replace the y in x/3 + 4y=30 with (2x-5) because they are equal. (y=2x-5)

    We have now have x/3+4(2x-5)=30. This looks a lot messier but we can simplify things. There are lots of ways of proceeding from here.
    x/3 looks nasty - to get rid of it multiply every term (peice of the equation) by 3

    x+(3*4(2x-5)=90
    x+12(2x-5)=90

    Next thing not to like about the equation is the brackets - essentially we want to count all the x's together. Getting rid of brackets is called multiplying out brackets. It looks strange but is just a property of the number system

    12(2x-5) is identical to 12*2x - 12*5 or 24x-60 in other words we can replace 12(2x-5) by 24x - 60

    we now have
    x+24x -60=90
    counting the x's together
    25x-60=90

    solving for x
    25x=150
    x=6

    Because we know x we can find y by substuting x=6 in 2x-y=5 (for example - you could use x/3 - 4y=30 but 2x-y=5 looks easier)

    12-y=5
    y=7

    Hope this helped - there's quite a lot of distractions in the question such as multiplying out etc.
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  3. #3
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    ... and then we remember to check our working by showing that the solution x=6, y=7 does indeed satisfy both equations (which it does).
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  4. #4
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    Thank you.

    So I can do the same thing to this problem:

    6x - y/4 = -9 and 3x + 2y = -30.
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  5. #5
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    Yeah. Try y=3x and 6x-2y+1=0. What does this tell you about the equations?
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  6. #6
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    Thanks for the help.
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