Answer
The student subtracted $y$ from both sides and added 1 to both sides. The student should have subtracted 1 from both sides (yielding $4x - y = -1$ instead of $4x - y = 1$).
Work Step by Step
$y = 4x + 1$
$y - 4x = 4x + 1 - 4x$
$-4x + y = 1$