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Math Help - Linear equations addition

  1. #1
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    Linear equations addition

    I'm probably making a silly mistake or Wolfram Alpha is lying to me.

    Question: Find the value of c and d.

    3d=13-2c
    \frac{3c+d}{2}=8

    Rearranged, simplified and multiply each equation by 2:

    6d+4c=26
    d+3c=16

    Now find the common multiple which in my case I will use 12:

    18d+12c=78
    -4d-12c=-64

    Then add them and find what d is worth:

    14d=14

    d=1

    Now when I plug this back into the equation, I will use the first one:

    3(1)+2c=13
    3+2(c)=13
    c=5

    d=1, c=5

    What am I doing wrong? Sorry if this is the long winded way to do it.
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  2. #2
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    Re: Linear equations addition

    You aren't doing anything wrong, that solution is correct. Perhaps you entered the fraction incorrectly into Wolfram Alpha
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  3. #3
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    Re: Linear equations addition

    You could have avoided one step and that is multiplying the first equation by 2.
    Re arrange the equations and we have
    2c + 3d = 13 ---- (1)
    3c + d = 16 ------(2)
    Multiply the second equation by -3 and re write the equations
    2c + 3d = 13 ---- (1)
    -9c -3 d = -48 ------(3)
    Add the equations and you have:
    -7c = -35 i.e., c = 5. Now get d from equation (2) we get d = 1
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