To figure out the answer to this problem you have to start by noticing that the equations are 'x+2y=6' and '2x+y=9'. Now take 2x+y=9 and subtract 2x from both sides. now y=9-2x so you can substitute y into the first equation. x+2(9-2x)=6. Distribute 2 by the 9 and -2x and you get x+18-4x=6. Add like terms and now you have -3x+18=6. Subtract 18 from both sides and you get -3x=-12 now divide -3 from both sides and you get 4=x. Now substitute 4 in for one of the equations 2(4)+y=9 and 2*4 is 8 so now you have 8+y=9 now you subtract 8 from both sides and you find the y=1 and x=4.