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# Confusing System of equations

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Solve the following where $$x_1$$ and $$y_1$$ are parameters/(not variables).

$$y = \frac{-x_1} {2 y_1} \cdot (x - x_1)$$
$$y = \frac{2 y_1}{x_1}(x - x_1/2)$$

May 20, 2019

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first thing to do is rewrite it so you don't have such confusion

$$x_1=a,~y_1=b\\~\\ y = -\dfrac{a}{2b}(x-a)\\~\\ y = \dfrac{2b}{a}\left(x - \dfrac a 2\right)$$

$$-\dfrac{a}{2b}(x-a)=\dfrac{2b}{a}\left(x-\dfrac a 2\right)\\~\\ -\dfrac{a^2}{4b^2}(x-a) =\left(x-\dfrac a 2\right)\\~\\ \dfrac{a^3}{4b^2}+ \dfrac a 2= x\left(1+\dfrac{a^2}{4b^2}\right)\\~\\ x = a\dfrac{\dfrac{a^2+2b^2}{4b^2}}{\dfrac{4b^2+a^2}{4b^2}}\\~\\ x = a \dfrac{a^2+2b^2}{a^2+4b^2}$$

Now you can substitute back in x1 for a and y1 for b

May 20, 2019