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Math Help - System of equations

  1. #1
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    System of equations

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  2. #2
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    Start by getting rid of fractions:
    42a - 7b + 7c = 61
    and
    21a - 21b - 14c = 43
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  3. #3
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    yea i did that already and ive gotten so many diffrent answers. and even plugged ihem back in to see if they r right... but no luck... but here is my last work. i found z and y which was z-25/91 and y=160/819 is that right?

    basically i tried to ways. one was making 1x+2y-2z=3 into everything equal to 1. and another i did was i just did a regular system of quation.. but yeah. help please.!
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  4. #4
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    Well, I'm not typing out the steps; but here's the solution:
    x = 143/91, b = 0, c = -65/91
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  5. #5
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    Smile

    hi
    your system is equivalent to,
    \left\{\begin{matrix}<br />
x+2y-2z=3\\ <br />
6x-y+z=\frac{61}{7}\\ <br />
3x-3y-2z=\frac{43}{7}<br />
\end{matrix}\right.
    your solution is  [x=\frac{11}{7},y=0,z=-\frac{5}{7}]
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  6. #6
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    (1): x + 2y - 2z = 3
    (2): 2x - \frac{1}{3}y + \frac{1}{3}z = \frac{61}{21}
    (3): \frac{3}{2}x - \frac{3}{2}y - z = \frac{43}{14}

    (1) x 42 \rightarrow 42x + 84y - 84z = 126
    (2) x 21 \rightarrow 42x - 7y + 7z = 61
    (3) x 28 \rightarrow 42x - 42y - 28z = 86

    (2) - (3) \rightarrow 35y + 35z = -25
    7y + yz = -5
    7z = -5 - 7y ...(4)

    From (1) \rightarrow 42x = 126 - 84y + 84z
    (4) into (1) \rightarrow 42x = 126 - 84y + 12(-5 - 7y)
    42x = 126 - 60 - 84y - 84y
    42x = 66 - 168y ...(5)

    (4) and (5) into (2) \rightarrow (66 - 168y) - 7y + (-5 - 7y) = 61
    182y = 0
    y = 0 ...(6)

    (6) into (4) \rightarrow 7z = -5 - 0
    z = -\frac{5}{7} ...(7)

    (6) and (7) into (1) \rightarrow x + 0 - 2(-\frac{5}{7}) = 3
    x = 3 - \frac{10}{7}
    x = \frac{11}{7}
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  7. #7
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    Quote Originally Posted by ukorov View Post
    (1): x + 2y - 2z = 3
    (2): 2x - \frac{1}{3}y + \frac{1}{3}z = \frac{61}{21}

    (1) x 42 \rightarrow 42x + 84y - 84z = 126
    (2) x 21 \rightarrow 42x - 7y + 7z = 61
    Much easier to leave (1) as is, and multiply (2) by 6:

    (1): x + 2y - 2z = 3
    (2):12x -2y+ 2z = 122/7
    13x = 3 + 122/7
    x = 11/7
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  8. #8
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    oh wth!? i actually did get that 11/7 and the zero but i got the 11/7 for z for some reason. and i also got the zero for the y, but i got both of those answers during diffrent tries of doing this problem.... but thxs everyone for the help!
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  9. #9
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    Quote Originally Posted by Wilmer View Post
    Much easier to leave (1) as is, and multiply (2) by 6:

    (1): x + 2y - 2z = 3
    (2):12x -2y+ 2z = 122/7
    13x = 3 + 122/7
    x = 11/7
    probably~ but I usually leave this "improvement" work to the question asker
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