We need to find the number of solutions to the system of equations: $9x - 3y = -6$ $5y = 15x + 10$

1. Problem Description

We need to find the number of solutions to the system of equations:

$9x - 3y = -6$

$5y = 15x + 10$

2. Solution Steps

First, let's simplify the first equation by dividing by 3:

$3x - y = -2$

We can rewrite this equation as:

$y = 3x + 2$

Next, let's simplify the second equation by dividing by 5:

$y = 3x + 2$

We observe that both equations are identical. This means they represent the same line. Therefore, there are infinitely many solutions.

3. Final Answer

Infinitely many solutions.