Show that the line $\displaystyle 5x+3y+ \lambda x $ = $\displaystyle 2 \lambda y -6 $ always passes from a fixed point . Determine the coordinate of the point.
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The equation can be written as $\displaystyle \lambda(x-2y)+5x+3y+6=0$ Then $\displaystyle \left\{\begin{array}{ll}x-2y=0\\5x+3y=-6\end{array}\right.$ Now solve the system.
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