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Math Help - Solving simultaneous equations

  1. #1
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    Solving simultaneous equations

    Just a question I have - I understand the how but not the why.

    if I have two equations of the line:

    2x-y=9 ... (1)
    3x+4y=-14 ... (2)

    I can solve this using the elimination method by multiplying equation (1) by 4 on both sides and thereby eliminating the y's when adding equation (2) to (1)
    - easy enough.

    BUT how does this work in finding the point of intersection? Wouldn't multiplying one equation by 4 change the line and therefore the point of intersection? That is wouldn't the value of x change since we are not doing anything to (2)?
    Last edited by oldjonesy; March 5th 2013 at 08:57 PM. Reason: spelling
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  2. #2
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    Re: Solving simultaneous equations

    Quote Originally Posted by oldjonesy View Post
    BUT how does this work in finding the point of intersection? Wouldn't multiplying one equation by 4 change the line and therefore the point of intersection? That is wouldn't the value of x change since we are not doing anything to (2)?
    Nope. If you multiply EVERYTHING by a constant number, it does not change anything. It will still be the equation of the same line.

    Suppose we have the equation:

    y = 3x + 5

    What happens if we multiply the equation by 4? We get:

    4y = 12x + 20

    So to plot the line, just find the x-intercept and the y-intercept and draw a line that goes through those 2 points.
    Have you tried plotting them? You'll notice that they're the same line.
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