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Thread: An Algebra 1 Question

  1. #1
    Junior Member
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    An Algebra 1 Question

    Hello all, thank you for your time.

    Solve the system:

    -x+3y=-1
    x+2y=4

    I understand how to do this, but my answer was not correct, the book said the answer was:
    (14/5,3/5) but I have no idea how it got that. I must have made an error in my work, but I'm not sure where.

    I started with x+2y=4 Subtracting 2y makes x=4-2y

    Then you plug that into the other equation and you get

    -4-2y+3y= -1
    Which simplifies to:
    -4+y=-1
    Adding 4 to both sides:
    y=3
    Plugging that into the other one:
    x+2x3=4
    Which simplifies to:
    x+6=4
    Subtract six:
    x=-2

    Which gives an answer of (-2,3) but I know this is not corrrect because it does not work when you plug that into x and y for the original two sets.

    Where am I making my error here?

    Thank you very much
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  2. #2
    MHF Contributor
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    You made your error on the first step. Given $\displaystyle x = 4 - 2y$ and $\displaystyle -x + 3y = -1$, you can substitute for x into the second equation: $\displaystyle -(4 - 2y) + 3y = -1$. This gives you $\displaystyle -4 + 2y + 3y = -1$, or $\displaystyle 5y - 4 = -1$.
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  3. #3
    Junior Member
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    Okay, just to make sure, same kind of problem with the -x thing i messed up

    Write the equation of the line that is parallel to line A and passes through Point P

    Line A=

    $\displaystyle y= -x+4$

    Point P= (-1,2)

    That would be:
    $\displaystyle y=-2-b$ right?
    Originally it would be +b (y=mx+b) but since it's -x the + changes to a - correct?
    If so, it would be
    $\displaystyle 2=-2-b$
    Add 2
    $\displaystyle 4=-b$
    $\displaystyle 4=b$

    and the answer would be
    $\displaystyle y=2x-4$

    correct?
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  4. #4
    Junior Member
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    Sorry made an error

    At the end I wrote

    $\displaystyle 4=-b$
    then
    $\displaystyle -4=b$
    so
    $\displaystyle y=2x-4$

    Forgot the negative on the second one
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  5. #5
    Senior Member
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    Melbourne
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    Write the equation of the line that is parallel to line A and passes through Point P

    Line A=



    Point P= (-1,2)
    A line parallel to A has the form y=-x +b.

    Substitute the x and y values of point P for x and y to find b.
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