why does 12x - 15y = 18 and 4x - 5y = 6 have infinite solutions

Answer 1

The system of equations has infinite solutions because the second equation is a multiple of the first equation.

If we multiply the first equation by 2, we get:

24x - 30y = 36

This is equivalent to the second equation, 4x - 5y = 6.

Therefore, any solution that satisfies the first equation will also satisfy the second equation. This means that there are an infinite number of solutions to the system of equations.