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Math Help - simoultaneous equation problem

  1. #1
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    simoultaneous equation problem

    hi guys, i tryed to solve this two equations using substitution but my x's ended up canceling out when trying to solve for x.

    6x - 2y = 14 eq 1
    -9x + 3y = 12 eq 2

    y = \frac {6x - 14}{2} eq 3 (re-arranged eq 1)

     -9x + 3(\frac {6x - 14}{2}) = 12 sub eq 3 into eq 2

     -18x + 3(6x - 14)= 24

     -18x + 18x - 42 = 24 that leaves me with no x

    any help much appreciated
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by jvignacio View Post
    hi guys, i tryed to solve this two equations using substitution but my x's ended up canceling out when trying to solve for x.

    6x - 2y = 14 eq 1
    -9x + 3y = 12 eq 2

    y = \frac {6x - 14}{2} eq 3 (re-arranged eq 1)

     -9x + 3(\frac {6x - 14}{2}) = 12 sub eq 3 into eq 2

     -18x + 3(6x - 14)= 24

     -18x + 18x - 42 = 24 that leaves me with no x

    any help much appreciated
    After a little manipulation, we have the system:

    \left\{\begin{array}{rcrcr}3x&-&y&=&7\\-3x&+&y&=&4\end{array}\right.

    Adding the two equations together yields 0=11, which is not true. Thus there are no solutions.

    In the future, if the variable disappears and you end up with some bizarre statement [like -5=3 or 0=2 , etc.], then you can conclude that there is no solution.

    Does this make sense?

    --Chris
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  3. #3
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    You assumed that the two curves intersected, but then you reached to a contradiction. Therefore, your original assumption is false.
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  4. #4
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    Quote Originally Posted by Chris L T521 View Post
    After a little manipulation, we have the system:

    \left\{\begin{array}{rcrcr}3x&-&y&=&7\\-3x&+&y&=&4\end{array}\right.

    Adding the two equations together yields 0=11, which is not true. Thus there are no solutions.

    In the future, if the variable disappears and you end up with some bizarre statement [like -5=3 or 0=2 , etc.], then you can conclude that there is no solution.

    Does this make sense?

    --Chris
    ahh yes so whenever the variable dissappears on me while trying to solve it, it means there are no solutions. okay thanks mate
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  5. #5
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    Quote Originally Posted by Chop Suey View Post
    You assumed that the two curves intersected, but then you reached to a contradiction. Therefore, your original assumption is false.
    yeah i understand, trying to do some tutorial questions set as practice. thanks mate
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  6. #6
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    Hello, jvignacio!

    Your work is correct!
    Here's another approach . . .


    I tried to solve this two equations using substitution
    but my x's ended up canceling out when trying to solve for x.

    \begin{array}{cccc}6x - 2y &=& 14 & [1] \\<br />
\text{-}9x + 3y &=& 12 & [2] \end{array}

    Graphic solution: we want the intersection of the two lines.

    \begin{array}{cc}\text{Solve [1] for }y\!: & y\:=\:3x - 7 \\<br />
\text{Solve [2] for }y\!: & y\:=\:3x + 4 \end{array}


    We have two lines: one has y-intercept -7, the other has y-intercept 4.
    Both have slope 3 . . . The lines are parallel.
    Code:
              | /
              |/    /
             4*    /
             /|   /
            / |  /
       ----/--+-/------
          /   |/
            -7*
             /|
            / |
              |

    Obviously, the line do not intersect.

    Therefore, the system has no solution.

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  7. #7
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    Quote Originally Posted by Soroban View Post
    Hello, jvignacio!

    Your work is correct!
    Here's another approach . . .


    Graphic solution: we want the intersection of the two lines.

    \begin{array}{cc}\text{Solve [1] for }y\!: & y\:=\:3x - 7 \\ \text{Solve [2] for }y\!: & y\:=\:3x + 4 \end{array}" alt="
    \text{Solve [2] for }y\!: & y\:=\:3x + 4 \end{array}" />


    We have two lines: one has y-intercept -7, the other has y-intercept 4.
    Both have slope 3 . . . The lines are parallel.
    Code:
              | /
              |/    /
             4*    /
             /|   /
            / |  /
       ----/--+-/------
          /   |/
            -7*
             /|
            / |
              |
    Obviously, the line do not intersect.

    Therefore, the system has no solution.
    soroban, thanks for that. really appreciate it!!!
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