To solve the system of equations:

2x + 5y = 10
3x - 2y = 1

We can use the elimination method by first multiplying the second equation by 5:

15x - 10y = 5

Now, we can add the first equation to this new equation:

17x = 15

Now we can solve for x:

17x = 15
x = 15/17

Next, we can substitute this value back into one of the original equations. Let's use the first equation:

2(15/17) + 5y = 10
30/17 + 5y = 10
5y = 170/17 - 30/17
5y = 140/17
y = 140/ (17 * 5)
y = 140/85

Therefore, the solution to the system of equations is: x = 15/17 and y = 140/85.