A1. What value must the number $a \in \mathbb{R}, a \neq 4$ and $a \neq 2$, have so that the lines with equations $a x-(a-2) y-2=0$ and $(a-1) x+(4-a) y+2=0$ intersect on the y-axis?
(A) -5
(B) 5
(C) -1
(D) -3
(E) 3
A1. If the lines intersect on the y-axis, the x-coordinate of the intersection is 0. We substitute $x=0$ into both line equations and simplify them to, for example, $-a y+2 y-2=0$ and $4 y-a y+2=0$. We get a system of two equations with two unknowns, which we solve in any way. The solutions are $y=-2$ and $a=3$. The correct answer is E.