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Math Help - Solving equations by substition help

  1. #1
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    Solving equations by substition help

    Here is the problem:

    solve these equations using substiution:
    2x+4y=8
    3x+2y+0

    I figured Y for the 2nd one first so I got
    2y=0+3x which equals y=3/2x

    substitute that into the first one

    2x +4(3/2x)=8

    2x+6x=8
    x=1

    put that into y=3/2x which I got 3/2 for Y

    then I went to check and only one worked, where am I going wrong? Thanks in advance!
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  2. #2
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    Hello, MathMack!

    A simple error . . .


    Solve by substiution: . \begin{array}{ccc}2x+4y &=&8 \\3x+2y&=&0 \end{array}

    I found y for the 2nd one and got: . y \:=\:\frac{3}{2}x

    It should have been: . y \:=\:{\bf{\color{red}-}}\frac{3}{2}x

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  3. #3
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    how did you get negative if you don't mind, and thanks for the help
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  4. #4
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    nevermind i got it! i'll work it out and see what happens
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  5. #5
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    when i go to check i get -8 for the 1st equation?
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  6. #6
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    nevermind, lol, forgot a negative, works out great I have another one i'm having trouble with, if you don't mind
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  7. #7
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    this one is by elimination

    3x+4y=2
    2x-3y= -10

    Where do I start?
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  8. #8
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    Quote Originally Posted by MathMack View Post
    Here is the problem:

    solve these equations using substiution:
    2x+4y=8
    3x+2y+0

    I figured Y for the 2nd one first so I got
    2y=0+3x which equals y=3/2x

    substitute that into the first one

    2x +4(3/2x)=8

    2x+6x=8
    x=1

    put that into y=3/2x which I got 3/2 for Y

    then I went to check and only one worked, where am I going wrong? Thanks in advance!
    2x + 4y = 8
    2x = 8 - 4y
    x = 4 - 2y

    Substitute into the other equation:

    3(4 - 2y) + 2y = 0
    12 - 6y + 2y = 0
    12 - 4y = 0
    12 = 4y
    y = 3

    And go back to the other equation:

    2x + 4(3) = 8
    2x + 12 = 8
    2x = -4
    x = -2


    this one is by elimination

    3x+4y=2
    2x-3y= -10

    Where do I start?
    You want to start by making the coefficients in front of one of the variables the same by multiplying each equation by a constant. I am going to make the coefficients of x equivalent.

    2(3x + 4y = 2) => 6x + 8y = 4
    3(2x - 3y = -10) => 6x - 9y = -30

    Now, subtract these two equations.

    (6x + 8y = 4)
    - (6x - 9y = -30) [Remember that subtracting a negative is equivalent to addition]
    --------------------
    0x + 17y = 34
    17y = 34
    y = 2

    Now, just like in substitution, use one of the original equations to solve for x.

    3x + 4(2) = 2
    3x + 8 = 2
    3x = -6
    x = -2

    Good luck. :>
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  9. #9
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    Thanks figured it all out, Thanks again!
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  10. #10
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    I have another one for you if you can help me please, the teacher says use whatever method I chose and the question is

    x+4y=9
    2x+y=4

    Don't know where to start. Thanks
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  11. #11
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    Nervmind, I figured it out!
    Last edited by MathMack; November 27th 2007 at 05:20 PM.
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