Find three solutions of 3x - y = 0. Why does its line pass through the origin?

Step 1. Three solutions. $y = 3x$. For $x = 0$, $1$ and $2$ we get $y = 0$, $3$ and $6$: the points $(0, 0)$, $(1, 3)$ and $(2, 6)$.

Step 2. The origin. The equation has no number standing alone. So $x = 0$, $y = 0$ makes it true: $3 \times 0 - 0 = 0$.