Step 1) Because the first equation is already solved for #y# we can substitute #-2x + 6# for #y# in the second equation and solve for #x#:
#2y + x = -5# becomes:
#2(-2x + 6) + x = -5#
#(2 xx -2x) + (2 xx 6) + x = -5#
#-4x + 12 + x = -5#
#-4x + x + 12 = -5#
#-3x + 12 = -5#
#-3x + 12 - color(red)(12) = -5 - color(red)(12)#
#-3x + 0 = -17#
#-3x = -17#
#(-3x)/color(red)(-3) = (-17)/color(red)(-3)#
#(color(red)(cancel(color(black)(-3)))x)/cancel(color(red)(-3)) = 17/3#
#x = 17/3#
Step 2) Subsitute #17/3# for #x# in the first equation and calculate #y#:
#y = -2x + 6# becomes:
#y = -34/3 + (3/3 xx 6)#
#y = -34/3 + 18/3#
#y = -16/3#
The solution is: #x = 17/3# and #y = -16/3# or #(17/3, -16/3)#