Step 1) Solve the first equation for #x#:
#2x - 2y = 0#
#2x - 2y + color(red)(2y) = 0 + color(red)(2y)#
#2x - 0 = 2y#
#2x = 2y#
#(2x)/color(red)(2) = (2y)/color(red)(2)#
#(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = (color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2))#
#x = y#
Step 2) Substitute #y# for #x# in the second equation and solve for #y#:
#4x + 9y = 0# becomes:
#4y + 9y = 0#
#(4 + 9)y = 0#
#13y = 0#
#(13y)/color(red)(13) = 0/color(red)(13)#
#(color(red)(cancel(color(black)(13)))y)/cancel(color(red)(13)) = 0#
#y = 0#
Step 3) Substitute #0# for #y# in the solution to the first equation at the end Step 1 to determine #x#:
#x = y# becomes:
#x = 0#
The Solution Is: #x = 0# and #y = 0# or #(0, 0)#