Step 1) Solve the first equation for #y#:
#2x - y = 4#
#2x - color(blue)(4) - y + color(red)(y) = 4 - color(blue)(4) + color(red)(y)#
#2x - 4 - 0 = 0 + y#
#2x - 4 = y#
#y = 2x - 4#
Step 2) Substitute #(2x - 4)# for #y# in the second equation and solve for #x#:
#7x + 3y = 27# becomes:
#7x + 3(2x - 4) = 27#
#7x + (3 xx 2x) - (3 xx 4) = 27#
#7x + 6x - 12 = 27#
#(7 + 6)x - 12 = 27#
#13x - 12 = 27#
#13x - 12 + color(red)(12) = 27 + color(red)(12)#
#13x - 0 = 39#
#13x = 39#
#(13x)/color(red)(13) = 39/color(red)(13)#
#(color(red)(cancel(color(black)(13)))x)/cancel(color(red)(13)) = 3#
#x = 3#
Step 3) Substitute #3# for #x# in the solution to the first equation at the end of Step 1 and calculate #y#:
#y = 2x - 4# becomes:
#y = (2 xx 3) - 4#
#y = 6 - 4#
#y = 2#
The Solution Is:
#x = 3# and #y = 2#
Or
#(3, 2)#
