Final answer:
After simplifying the given equations, we find that they are identical, meaning they represent the same line. Hence, the system of equations has infinitely many solutions.
Step-by-step explanation:
To determine how many solutions the system has with the equations 4x−10y=−20 and 6x−15y=−30, we can compare the two equations to see if they are equivalent or distinct. Both equations can be simplified by dividing by their greatest common divisors. For the first equation, dividing both sides by 2 gives us 2x − 5y = −10, and for the second equation, dividing both sides by 3 gives us 2x − 5y = −10 as well. Since both simplified equations are identical, this tells us that the two original equations are also identical, representing the same line.
Therefore, the system of equations has infinitely many solutions because any solution that works for one equation will also work for the other, since they are the same line.