A/2 - 3/b = 5/6

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

From equation (a), we have:

a/2 - 3/b = 5/6

Multiplying both sides by 2b, we get:

ab - 6 = 5b/6

Multiplying both sides by 6, we get:

6ab - 36 = 5b

Rearranging the equation, we have:

6ab - 5b = 36

Factoring out b, we get:

b(6a - 5) = 36

Dividing both sides by (6a - 5), we get:

b = 36/(6a - 5)

Now, we can substitute this value of b into equation (b):

a/3 - 1/(36/(6a - 5)) = 4/15

Simplifying the equation, we get:

a/3 - (6a - 5)/36 = 4/15

Multiplying both sides by 36, we get:

12a - (6a - 5) = 48/15

Simplifying the equation, we get:

12a - 6a + 5 = 16/5

Combining like terms, we get:

6a + 5 = 16/5

Multiplying both sides by 5, we get:

30a + 25 = 16

Subtracting 25 from both sides, we get:

30a = -9

Dividing both sides by 30, we get:

a = -9/30

Simplifying the fraction, we get:

a = -3/10

Now, we can substitute this value of a into equation (a) to find the value of b:

(-3/10)/2 - 3/b = 5/6

Multiplying both sides by 2, we get:

-3/10 - 6/b = 5/3

Multiplying both sides by 30b, we get:

-9b - 180 = 50b

Adding 9b to both sides, we get:

-180 = 59b

Dividing both sides by 59, we get:

b = -180/59

Therefore, the solution to the system of equations is a = -3/10 and b = -180/59.