Assuming your answer is correct plug ' x=-3/4y+2' into '9x+3y=18' and solve. If this is the correct answer you should get identity. 

9(-3/4y+2) + 3y = 18

Instead, you get 'y = 0' meaning the above solution is correct only when y = 0, not for all real numbers y.

By plugging 

you will get '18 =18' which is valid for every 'y' thus this is the correct solution.