Step 1) Solve the second equation for #x#:
#x - 2y = 8#
#x - 2y + color(red)(2y) = 8 + color(red)(2y)#
#x - 0 = 8 + 2y#
#x = 8 + 2y#
Step 2) Substitute #8 + 2y# for #x# in the first equation and solve for #y#:
#-4x - 14y = 28# becomes:
#-4(8 + 2y) - 14y = 28#
#(-4 xx 8) + (-4 xx 2y) - 14y = 28#
#-32 - 8y - 14y = 28#
#-32 - 22y = 28#
#color(red)(32) - 32 - 22y = color(red)(32) + 28#
#0 - 22y = 60#
#-22y = 60#
#(-22y)/color(red)(-22) = 60/color(red)(-22)#
#(color(red)(cancel(color(black)(-22)))y)/cancel(color(red)(-22)) = (2 xx 30)/color(red)(2 xx -11)#
#y = (color(red)(cancel(color(black)(2))) xx 30)/color(red)(cancel(2) xx -11)#
#y = -30/11#
Step 3) Substitute #-30/11# for #y# in the solution to the second equation at the end of Step 1 and calculate #x#:
#x = 8 + 2y# becomes:
#x = 8 + (2 xx -30/11)#
#x = (11/11 xx 8) - 60/11#
#x = 88/11 - 60/11#
#x = (88 - 60)/11#
#x = 28/11#
The solution is: #x = 28/11# and #y = -30/11# or #(28/11, -30/11)#
