How many solutions does this equation have

Question

12x-15y=18
4x-5y=6

Answer 1

To determine the number of solutions, we need to examine their relationship.

Let's multiply the first equation by 4 and the second equation by 3 to make the coefficients of x equal.

The new equations become:

48x - 60y = 72
12x - 15y = 18

To simplify, we can divide all the terms by 3 in the first equation:

16x - 20y = 24

Now, we can see that both equations are the same. They represent the same line.

Since the two equations represent the same line, there are infinitely many solutions.