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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- May 3rd 2009, 11:02 PMzorroDetermine the coordinates of the point
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. - May 4th 2009, 07:28 AMred_dog
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.