Step 1) Solve the first equation for #y#:
#2x + y - 4 = 0#
#2x - color(red)(2x) + y - 4 + color(blue)(4) = -color(red)(2x) + color(blue)(4)#
#0 + y - 0 = -2x + 4#
#y = -2x + 4#
Step 2) Substitute #(-2x + 4)# for #y# in the second equation and solve for #x#:
#2x - y = 4# becomes:
#2x - (-2x + 4) = 4#
#2x + 2x - 4 = 4#
#(2 + 2)x - 4 = 4#
#4x - 4 = 4#
#4x - 4 + color(red)(4) = 4 + color(red)(4)#
#4x - 0 = 8#
#4x = 8#
#(4x)/color(red)(4) = 8/color(red)(4)#
#(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = 2#
#x = 2#
Step 3) Substitute #2# 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 2) + 4#
#y = -4 + 4#
#y = 0#
The Solution Is:
#x = 2# and #y = 0#
Or
#(2, 0)#
