To solve this system of equations, we can use the method of substitution or elimination.

Let's use the elimination method.

First, we can simplify the first equation by dividing by 3:
5x - 3y = 8
(5/3)x - y = 8/3

Now, let's multiply the second equation by 1/3 to match the coefficient of y in the first equation:
15x -9y = 8
(15/3)x - 3y = 8/3

Now, we can subtract the first equation from the second equation to eliminate y:
(15/3)x - 3y - (5/3)x + y = 8/3 - 8/3
(10/3)x - 2y = 0

Now we have a new equation:
(10/3)x - 2y = 0

To solve for x, we can isolate x in terms of y:
(10/3)x = 2y
x = (3/10) * 2y
x = 6y/10
x = 3y/5

Now we can substitute this value of x back into the first equation to solve for y:
5(3y/5) - 3y = 8
3y - 3y = 8
0 = 8

Since this equation is not true, it means that the system of equations is inconsistent and there is no solution.