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

Let's use the method of substitution:

From the second equation, we can solve for x:

-x - y = 3
-x = 3 + y
x = -3 - y

Now we substitute this value of x into the first equation:

-(-3 - y) + 2y = 1
3 + y + 2y = 1
3 + 3y = 1
3y = 1 - 3
3y = -2
y = -2/3

Now substitute this value of y back into the second equation to find x:

-x - (-2/3) = 3
-x + 2/3 = 3
-x = 3 - 2/3
-x = 9/3 - 2/3
-x = 7/3
x = -7/3

Therefore, the solution to the system of equations is x = -7/3 and y = -2/3.