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Math Help - Solve for x

  1. #1
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    Solve for x

    Its actually a trig question, but I'm having trouble with the algebra.

    Solve for x
    1st equation: x + y = 5 and 2nd equation: x^2/16 + y^2/9 = 1

    My work so far...

    sub y = x - 5 in to 2nd equation

    x^2/16 + (x-5)^2/9 = 1

    What do we do from here? Find the common denominator (144) and...

    Thanks in advance
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  2. #2
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    Re: Solve for x

    Actually y = 5-x but it doesn't really matter.

    Multiply both sides by 144, expand stuff, solve for x. Then plug your solution into x+y = 5 to find y.
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  3. #3
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    Lightbulb Re: Solve for x

    Attached Thumbnails Attached Thumbnails Solve for x-solve-x.png  
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  4. #4
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    Re: Solve for x

    "Multiply both sides by 144, expand stuff, solve for x" is the part I'm struggling with...
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  5. #5
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    Re: Solve for x

    Quote Originally Posted by durrrr View Post
    "Multiply both sides by 144, expand stuff, solve for x" is the part I'm struggling with...
    Show us what you've done then...
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  6. #6
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    Re: Solve for x

    1st equation: x + y = 5 and 2nd equation: x^2/16 + y^2/9 = 1

    y = x - 5

    Sub into 2nd equation...

    x^2/16 + (x-5)^2/9 = 1

    9x^2/144 + ???/144 = 1

    Sorry, I'm obviously not very good at math. I don't know what to do to the (x - 5). I'd really appreciate if somebody could finish the equation in baby steps. I understand the concept behind tangents and the actual question, there are obviously just gaping holes in my basic math knowledge when it comes to completing the solution.
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  7. #7
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    Re: Solve for x

    Quote Originally Posted by durrrr View Post
    1st equation: x + y = 5 and 2nd equation: x^2/16 + y^2/9 = 1

    y = x - 5

    Sub into 2nd equation...

    x^2/16 + (x-5)^2/9 = 1

    9x^2/144 + ???/144 = 1

    Sorry, I'm obviously not very good at math. I don't know what to do to the (x - 5). I'd really appreciate if somebody could finish the equation in baby steps. I understand the concept behind tangents and the actual question, there are obviously just gaping holes in my basic math knowledge when it comes to completing the solution.
    Well if you've started by getting a common denominator of 144, then the numerator of the second equation needs to be multiplied by \displaystyle \begin{align*} 16 \end{align*}, giving \displaystyle \begin{align*} 16(x - 5)^2 \end{align*}. Now to expand the \displaystyle \begin{align*} (x - 5)^2 \end{align*}, use \displaystyle \begin{align*} (a - b)^2 = a^2 - 2ab + b^2 \end{align*}.
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