How many solutions does the system of equations have 9x - 12y = 24 and 3X = 4y

To determine the number of solutions this system of equations has, we can first simplify the second equation:

3X = 4y

Dividing both sides of the equation by 4, we get:

3/4 X = y

Now we substitute this value for y in the first equation:

9x - 12(3/4 X) = 24

Expanding and simplifying, we have:

9x - (36/4)x = 24
9x - 9x = 24

This equation simplifies to 0 = 24, which is not a true statement. Therefore, these equations are inconsistent, and the system has no solutions.