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Math Help - simultaneous equations

  1. #1
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    simultaneous equations

    hi, i am doing a electronic engineering course and have come up with the simultaneous equations thati need to answer. any help on it? many thanks. liam



    10x - 10 + 20y - 20 = 0

    +20-20y+40(y-x)= 0
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    Hello,

    Quote Originally Posted by djstar View Post
    hi, i am doing a electronic engineering course and have come up with the simultaneous equations thati need to answer. any help on it? many thanks. liam



    10x - 10 + 20y - 20 = 0

    +20-20y+40(y-x)= 0
    In the first equation, divide by 10, then group :

    10x-10+20y-20=0 \Longleftrightarrow x-1+2y-2=0 \Longleftrightarrow x-3+2y=0

    In the second equation, divide by 20, then develop :

    20-20y+40(y-x)=0 \Longleftrightarrow 1-y+2(y-x)=0 \Longleftrightarrow 1+y-2x=0 \implies y=2x-1

    Therefore, by substituting in the first equation :

    x-3+2(2x-1)=0 \implies x-3+4x-2=0 \implies 5x-5=0 \implies \boxed{x=1}

    y=2x-1=2(1)-1=\boxed{1}
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  3. #3
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    Quote Originally Posted by djstar View Post
    hi, i am doing a electronic engineering course and have come up with the simultaneous equations thati need to answer. any help on it? many thanks. liam



    10x - 10 + 20y - 20 = 0

    +20-20y+40(y-x)= 0
    Simplifying your 2 equations, you get:

    10x + 20y = 30

    -40x + 20y = -20

    From here, I know 3 ways to solve. For the elimination method, go here:

    2 Unknowns by Elimination Calculator

    Enter those 2 equations and press the solve button.

    I get (x,y) = (1,1) Plugging those back into the original equations, those work.

    You could also use the substitution method here:

    2 Unknowns by Substitution Calculator

    or Cramer's method here:

    2 Unknown Cramer's Method Calculator

    Let me know if you have questions.
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