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

Multiply the first equation by 3:
3(3x + y = 2)
This gives:
9x + 3y = 6

Let's rewrite the second equation:
5x - 3y = 8

Add the two equations together:
9x + 3y + 5x - 3y = 6 + 8
14x = 14
Divide by 14 on both sides to solve for x:
x = 1

Substitute the value of x back into either of the original equations. Let's use the first equation:
3(1) + y = 2
3 + y = 2
Subtract 3 from both sides to solve for y:
y = -1

Therefore, the solution to the system of equations is x = 1, y = -1.