Step 1) Solve the second equation for #y#:
#8x + y - color(red)(8x) = 18 - color(red)(8x)#
#8x - color(red)(8x) + y = 18 - color(red)(8x)#
#0 + y = 18 - 8x#
#y = 18 - 8x#
Step 2) Substitute #color(red)(18 - 8x)# for #y# in the first equation and solve for #x#:
#4x - (color(red)(18 - 8x)) = 0#
#4x - color(red)(18 + 8x) = 0#
#4x + 8x - 18 = 0#
#12x - 18 = 0#
#12x - 18 + color(red)(18) = 0 + color(red)(18)#
#12x - 0 = 18#
#12x = 18#
#(12x)/color(red)(12) = 18/color(red)(12)#
#(color(red)(cancel(color(black)(12)))x)/cancel(color(red)(12)) = (6 xx 3)/(6 xx 2)#
#x = (cancel(6) xx 3)/(cancel(6) xx 2)#
#x = 3/2#
Step 3) Substitute #color(red)(3/2)# for #x# in the solution to the second equation in Step 1 to calculate #y#
#y = 18 - (8 xx color(red)(3/2))#
#y = 18 - (color(red)(cancel(color(black)(8)))4 xx color(red)(3)/cancel(color(red)(2)))#
#y = 18 - (4 xx 3)#
#y = 18 - 12#
#y = 6#
