You could solve this system of equations by using the multiplication method.
To do that, start by multiplying both sides of the first equation by #-3#.
#-3 * (x+y) = -3 * (-7)#
#-3x - 3y = 21#
The system of equations will now be
#{(-3x -3y = 21), (3x + y = -9) :}#
Next, add left sides and the right sides of the two equations separately to eliminate the terms that contain #x#
#-color(red)(cancel(color(black)(3x))) - 3y + color(red)(cancel(color(black)(3x))) + y = 21 - 9#
#-2y = 12#
Divide both sides of the equation by #-2# to get the value of #y#
#(-color(red)(cancel(color(black)(2)))y)/(-color(red)(cancel(color(black)(2)))) = 12/(-2) => y = color(green)(-6)#
Now that you know the value of #y#, use it in one of the two equations to determine the value of #x#
#3x + y = -9#
#3x + (-6) = -9#
This is equivalent to
#3x = -9 + 6 = -3#
Now divide both sides of this equation by #3# to get the value of #x#
#(color(red)(cancel(color(black)(3)))x)/color(red)(cancel(color(black)(3))) = (-3)/3 => x = color(green)(-1)#
The two solutions are
#{(x=-1), (y=-6) :}#