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

Let's use the substitution method.

From the first equation, we can express y in terms of x:

y = x - 3

Now we substitute this expression for y in the second equation:

2x + (x - 3) = 5
2x + x - 3 = 5
3x - 3 = 5
3x = 8
x = 8/3

Now that we have found the value of x, we can substitute it back into the first equation to find the value of y:

x - y = 3
8/3 - y = 3
y = 8/3 - 3
y = 8/3 - 9/3
y = -1/3

Therefore, the solution to the system of equations is x = 8/3 and y = -1/3.