# Thread: Determine the coordinates of the point

1. ## Determine the coordinates of the point

Show that the line $
5x+3y+ \lambda x
$
= $
2 \lambda y -6
$
always passes from a fixed point . Determine the coordinate of the point.

2. The equation can be written as

$\lambda(x-2y)+5x+3y+6=0$

Then $\left\{\begin{array}{ll}x-2y=0\\5x+3y=-6\end{array}\right.$

Now solve the system.