Why is $y = - 1/\lambda $ in $2\lambda x+2\lambda y+1=0$?

Question

In a textbook they give $2\lambda x+2\lambda y+1=0$ $y=-1/\lambda $

$2\lambda x+6\lambda y+5=0$ $x=1/2\lambda $

It might be very easy but I don't understand that.

Answer 1

You did not write the equations in the correct order: From: $$2\lambda x+2\lambda y+1=0\\2\lambda x+6\lambda y+5=0$$ You subtract the first equation from the second and you get $$4\lambda y+4=0$$ Which is $$y=-\frac 1\lambda$$ Now plug this value in the first equation and you get $$2\lambda x-2+1=0$$ or $$x=\frac1{2\lambda}$$