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Thread: Solving a system of equations

  1. #1
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    Solving a system of equations

    So the question is Solve for the system of equations:

    y =3x - 10 (-4,-2)

    4x-3y=-19
    2x+y=13
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  2. #2
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    Re: Solving a system of equations

    You have copied (and high-lighted) the last line of problem #10 as if it were part of problem #11. Did you realize that? Problem #11 asks you to solve the two equations 4x- 3y= -19 and 2x+ y= 13. Multiply the second equation by 3, 6x+ 3y= 39, and add that to the first equation.
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    Re: Solving a system of equations

    Thank you I didn’t catch that error but that would’ve simplified everything! I appreciate the help, thank you once again
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  4. #4
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    Re: Solving a system of equations

    Where did the 3 come from though like why multiply by 3?
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    Re: Solving a system of equations

    Quote Originally Posted by Eddyrodriguez View Post
    Where did the 3 come from though like why multiply by 3?
    That technique is trying to eliminate one of the variables. So, the first equation has -3y. The second equation has y. If you multiply the second equation by 3, you have a -3y in the first equation and a +3y in the modified second equation, so now when you add them, you have 0y (this gives an equation only in x).

    Another method: In the second equation, solve for y in terms of x (I choose the second equation because the coefficient of y is 1):

    $y = 13-2x$

    Now, plug that into the first equation:

    $4x-3(13-2x)=-19$

    After multiplying out, you can solve for $x$ since it is an equation in one variable. Once you know x, plug it into the formula you just created for y.
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  6. #6
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    Re: Solving a system of equations

    Quote Originally Posted by Eddyrodriguez View Post
    Where did the 3 come from though like why multiply by 3?
    These are your equations:
    4x-3y=-19 [1]
    2x+y=13 [2]

    Multiply [2] by 3 and you now have:
    4x-3y=-19 [1]
    6x+3y= 39 [2]

    Add 'em up:
    4x-3y=-19 [1]
    6x+3y=39 [2]
    -----------------
    10x + 0 = 20
    So x = 2

    Are you saying that your teacher never taught that?
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  7. #7
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    Re: Solving a system of equations

    Quote Originally Posted by Eddyrodriguez View Post
    Where did the 3 come from though like why multiply by 3?
    The first equation had "-3y". The second equation had "+ y". Multiplying the second equation by 3 changes that to "+ 3y" and adding "-3y+ 3y" eliminates "y" from the equation.
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