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Math Help - [SOLVED] Need help solving a system of equation

  1. #1
    Junior Member Rheanna's Avatar
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    [SOLVED] Need help solving a system of equation

    Trying to figure out how they are coming up with 2,3 and not 5,3
    Thanks

    4x+3y=17
    2x+3y=13
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  2. #2
    Junior Member Rheanna's Avatar
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    Nevermind, rather than adding the bottom equation they subtracted it which makes it come out to 2,3
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  3. #3
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    subtract the 2nd equation from the 1st

    you'll get 2x = 4

    after solving you'll get x= 2

    and put the value of x in any of the above eqn you'll get y
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  4. #4
    Senior Member pacman's Avatar
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    4x+3y=17
    2x+3y=13
    ______________________________________________

    4x+3y=17
    (2x+3y=13) - multi ply by -2 to the x terms. Now add . . . .

    4x + 3y = 17
    -4x - 6y = -26
    0 - 3y = -9

    y =-9/-3 = 3

    Next,

    4x+3y=17
    2x+3y=13, multiply by -1 to eliminate y terms,

    4x +3y = 17
    -2x - 3y = -13 then add,

    ?
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  5. #5
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    Quote Originally Posted by Rheanna View Post
    Nevermind, rather than adding the bottom equation they subtracted it which makes it come out to 2,3
    Just a note: It should make no difference whether they add or substract the equations -- either way there is one unique solution.

    If you choose to add them, you get:

    4x+3y+2x+3y=17+13 \Rightarrow 6x+6y = 30 \Rightarrow 6(x+y) = 6*5 \Rightarrow x+y = 5 \Rightarrow x = 5-y

    Now substitute that into either equation, let's say the first:

    4(5-y)+3y = 17 \Rightarrow 20-4y+3y=17\Rightarrow -y = -3 \Rightarrow y = 3 \Rightarrow x + 3 = 5  \Rightarrow \boxed{x=2, y=3}
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