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

Using substitution:
From the first equation, we can express x in terms of y:
5x + 6y = 9
5x = 9 - 6y
x = (9 - 6y) / 5

Now substitute this expression for x into the second equation:
20((9 - 6y) / 5) + 17y = 15
Multiplying both sides by 5 to get rid of the fractions:
4(9 - 6y) + 17y = 75
36 - 24y + 17y = 75
-7y = 39
y = -39/7

Now, substitute the value of y back into the first equation to find x:
5x + 6(-39/7) = 9
5x - 234/7 = 9
5x = 9 + 234/7
5x = 63/7 + 234/7
5x = 297/7
x = 297/35

Therefore, the solution to the system of equations is:
x = 297/35
y = -39/7

Using elimination:
To eliminate one variable, multiply the first equation by 17 and the second equation by 6:
85x + 102y = 153
120x + 102y = 90

Subtract the second equation from the first:
(85 - 120)x = 153 - 90
-35x = 63
x = -63/35
x = -9/5

Now substitute x back into the first equation to solve for y:
5(-9/5) + 6y = 9
-9 + 6y = 9
6y = 18
y = 18/6
y = 3

Therefore, the solution to the system of equations is:
x = -9/5
y = 3