How many solutions does the pair $3x - 4y = 10$ and $9x - 12y = 30$ have?

Explanation

1. 01

   Compare ratios: $\frac{3}{9} = \frac{1}{3}$, $\frac{-4}{-12} = \frac{1}{3}$, $\frac{10}{30} = \frac{1}{3}$.

2. 02

   All three ratios are equal, so the second equation is just the first multiplied by 3.

3. 03

   Both equations describe the same line, so every point on it is a solution: infinitely many.