In elimination method what we try to do is eliminate one of the variable, whether #x# or #y#.
Using #x-# Observe that coefficient of #x# in both the equations is same i.e. #-1#. Hence if we subtract one equation from other #x# will get eliminated.
Therefore #-x-y-(-x+3y)=11-(-13)#
or #-x-y+x-3y=11+13#
or #-cancelx-y+cancelx-3y=24#
or #-4y=-24# i.e. #y=24/(-4)=-6#
Putting this in first equatin we get #-x-(-6)=11#
or #-x+6=11# i.e. #-x=11-6=5# or #x=-5#
and solution is #x=-5# and #y=-6#
Using #y-# Observe that coefficient of #y# in both the equations is different. While in first equation it is #-1# in second equation it is #3#. Hence we multiply first by #3# and add it to second equation and #y# will get eliminated.
#3xx(-x-y)+(-x+3y)=3xx11+(-13)#
or #-3x-3y-x+3y==20#
or #-3x-cancel(3y)-x+cancel(3y)=20#
or #-4x=-20# i.e. #x=20/(-4)=-5#
Putting this in first we get #-(-5)-y=11#
i.e. #5-y=11#
or #-y=11-5=6# i.e. #y=-6#