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Math Help - Difficulty on solving a pair of simultaneous equations

  1. #1
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    Difficulty on solving a pair of simultaneous equations

    Hi all, new here. I've recently began a home study AS/A2 course in mechanical mathematics after being outside of formal education for almost 7 years. I'm currently having problems with remembering methods taught at basic AS level, and in particular the solution and method to this pair of simultaneous equations:

    5x + 4y + 5 = 3x - 7y, 4(x+3y) + 3 = 5x

    Help would be greatly appreciated!
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  2. #2
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    Re: Difficulty on solving a pair of simultaneous equations

    Quote Originally Posted by FH88 View Post
    Hi all, new here. I've recently began a home study AS/A2 course in mechanical mathematics after being outside of formal education for almost 7 years. I'm currently having problems with remembering methods taught at basic AS level, and in particular the solution and method to this pair of simultaneous equations:

    5x + 4y + 5 = 3x - 7y, 4(x+3y) + 3 = 5x

    Help would be greatly appreciated!
    I suggest you start by simplfying the equations separately:
    5x+ 4y+ 5= 3x- 7y: subtract 3x- 7y+ 5 from both sides
    4(x+ 3y)+ 3= 5x: multiply the 4 by both x and 3y then subtract 5x+ 3 from both sides.
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  3. #3
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    Re: Difficulty on solving a pair of simultaneous equations

    Quote Originally Posted by HallsofIvy View Post
    I suggest you start by simplfying the equations separately:
    5x+ 4y+ 5= 3x- 7y: subtract 3x- 7y+ 5 from both sides
    4(x+ 3y)+ 3= 5x: multiply the 4 by both x and 3y then subtract 5x+ 3 from both sides.
    Ok, thanks for your reply, so after that and using the elimination method I have:

    31x = -27
    x = - 31/27

    Is this ok?
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  4. #4
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    Re: Difficulty on solving a pair of simultaneous equations

    No. You also need to solve for y.
    Check if your solution is correct yourself: substitute your answer back in one of the equations.
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  5. #5
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    Re: Difficulty on solving a pair of simultaneous equations

    Ok, I think I've cracked it:

    I first simplified the equations to;

    2x + 11y = -5,
    -x + 12y = -3

    Then made the coefficients of y the same value:

    24x + 132y = -60,
    -11x + 132y = -33

    then subtracted leaving with the value of x:

    35x = -27,
    x = -27/35

    substituted back into the first equation, giving me the value of y:

    5 -54/35 = -11y
    y = -11/35

    Is this ok?
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  6. #6
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    Re: Difficulty on solving a pair of simultaneous equations

    You can check yourself...SUBSTITUTE.
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