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

First, let's rewrite the equations in standard form:
1) 3x - 5y = 1
2) 2x + y = 45

To eliminate y, we can multiply equation 2 by 5 and add it to equation 1:

13x = 226

Now, divide both sides by 13 to solve for x:
x = 226 / 13
x = 17.38 (rounded to two decimal places)

Now that we have found the value of x, we can substitute it back into either of the original equations to solve for y. Let's substitute it into equation 2:

2(17.38) + y = 45
34.76 + y = 45
y = 45 - 34.76
y = 10.24

Therefore, the solution to the system of equations is:
x = 17.38
y = 10.24