I was solving $19x\equiv42 \mod(50)$
I had used these following theorem 
SO as $19 \cdot 5=95 \equiv -5 \pmod{50}$
and $42 \cdot 5\equiv -8 \cdot 5 \pmod{50} \equiv -40 \pmod{50}$
SO $-5x\equiv -40 \pmod{50}$ which means $5x\equiv 40 \pmod{50}$ by using above theorem
$x\equiv 8 \pmod{10}$ so my answer should be $8,18,28,38,48$
But answer is only $18 \pmod{50}$.
AS theorem statement is if and only if all solution must be there
Where is my mistake?
Is there is any other short method to solve equation?
Any help will be appreciated.