hello anyone, i have a problem on the determinant

here are 3 liner equations:

y=3

y-x=0

y-3x-6=0

there has a point (3,3) which can be passed through by these 3 lines

the determinant of the coefficients of these three lines is zero.

why? Is it always true if any 3 lines are concurrent? Thank you!

p.s please forgive my poor English.