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

From the first equation, we have x + y = -1. Solving for x, we get x = -1 - y.

Substituting this value of x into the second equation, we have m(-1 - y) + y = 2m.

Expanding the equation, we get -m - my + y = 2m.

Combining like terms, we have (-m + y) - my = 2m.

Rearranging the equation, we get -my + y - m = 2m.

Factoring out y, we have y(-m + 1) - m = 2m.

Simplifying further, we get y(-m + 1) = 3m.

Dividing both sides by (-m + 1), we have y = (3m)/(-m + 1).

Now, substituting this value of y back into the first equation, we have x + (3m)/(-m + 1) = -1.

Multiplying both sides by (-m + 1), we have x(-m + 1) + 3m = -m + 1.

Expanding the equation, we get -xm + x + 3m = -m + 1.

Combining like terms, we have (-xm + 3m) + x = -m + 1.

Rearranging the equation, we have -xm + 3m + x = -m + 1.

Factoring out x, we have x(-m + 3) + 3m = -m + 1.

Simplifying further, we get x(-m + 3) = -4m + 1.

Dividing both sides by (-m + 3), we have x = (-4m + 1)/(-m + 3).

Therefore, the solution to the system of equations is x = (-4m + 1)/(-m + 3) and y = (3m)/(-m + 1).