Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution.

-20x + 30y = - 3

8x - 12y = - 3

No solution.

Step-by-step explanation:

A system has only one solution if it ends at ax = b, in which a is different than 0.

If it ends at 0x = 0, the system has infinitely many solutions.

If it ends at a division by 0, or 0 = constant (different than 0), the system is inconsistent.

Our system is:

-20x + 30y = - 3

8x - 12y = - 3

I am going to multiply the top equations by 2 and the bottom equation by 5, and add them. So

-40x + 60y = - 6

40x - 60y = - 15

So

-40x + 40x + 60y - 60y = - 6 - 15

0x + 0y = - 21

We cannot divide 21 by 0, which means that this system of equations has no solution.