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I found this page on the intersection of 2 lines. And I'm really surprised about going from:

$$\begin{align*} x_1 + u_a (x_2 - x_1) &= x_3 + u_b (x_4 - x_3) \\\ y_1 + u_a (y_2 - y_1) &= y_3 + u_b (y_4 - y_3) \end{align*}$$

to this

$$\begin{align*} u_a &= \frac{(x_4 - x_3)(y_1 - y_3) - (y_4-y_3)(x_1-x_3)}{(y_4-y_3)(x_2-x_1)-(x_4-x_3)(y_2-y_1)} \\\ u_b &= \frac{(x_2-x_1)(y_1-y_3)-(y_2-y_1)(x_1-x_3)}{(y_4-y_3)(x_2-x_1)-(x_4-x_3)(y_2-y_1)} \end{align*}$$

Could somebody carry it for me cause I always fail and get other final equation.

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    typo in the title2011-08-20
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    @Pierre, took it upon myself to fix it.2011-08-20
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    A useful keyword in this context is *Cramer's rule* and a detailed answer to your question is written here: http://en.wikipedia.org/wiki/Cramer%27s_rule#Explicit_formulas_for_small_systems2011-08-20
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    @Gerry: Thanks! (I don't have edit privileges.)2011-08-20

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