To solve the system of equations:

2x + 5y = 9 ...(1)
3x + 2y = 6 ...(2)

There are multiple methods to solve this system, but I will use the method of substitution. Here's how:

From equation (2), solve for x in terms of y:
3x = 6 - 2y
x = (6 - 2y) / 3

Substitute this value of x in equation (1):
2((6 - 2y) / 3) + 5y = 9

Now, we can simplify and solve for y:
(12 - 4y) / 3 + 5y = 9
12 - 4y + 15y = 27
11y = 15
y = 15 / 11

Substitute the value of y back into equation (2) to find x:
3x + 2(15 / 11) = 6
3x + 30 / 11 = 6
3x = 6 - 30 / 11
3x = (66 - 30) / 11
3x = 36 / 11
x = 12 / 11

Therefore, the solution to the system of equations is:
x = 12 / 11
y = 15 / 11