(x, y) = (-3, 2)
The two equations are recognizable as expressing the sum and difference of the two variables. Such a set of equations is easily solved by the "elimination" method.
The y-variables have opposite coefficients in the two equations, so that variable can be eliminated by adding the two equations:
(x -y) +(x +y) = (-5) +(-1)
2x = -6 . . . . . . . simplify
x = -3 . . . . . . divide by 2
The x-variables have the same coefficient in the two equations, so that variable can be eliminated by subtracting one equation from the other. We choose to subtract the first equation so the result has a positive coefficient for y.
(x +y) -(x -y) = (-1) -(-5)
2y = 4 . . . . . . . simplify
y = 2 . . . . . . divide by 2
The solution to the system of equations is (x, y) = (-3, 2).