Solve equations 2x+y=9 and x+2y=6 to find x and y.

First of all we need to rearrange the equations in a way which allows us to get rid of either the x or y variable.

To do this we need to have either the same number of x's or same number of y's in both equations. 

So we can change x+2y=6 to 2x+4y=12 by multiplying the equation by 2.

Then we can do 2x+4y=12 - 2x+y=9 to give us 3y=3 and therefore y=1.

Now to find x we can substitute our value for y back into one of our original equations, for example x+2y=6. to give us x+2=6, which solves through to x=4.

Finally we can check our answer by substituting our x and y values back into the other original equation and checking it makes sense. 2x+y = 9 becomes 8+1=9, so we have solved correctly.

Therefore our final answer is x = 4 and y = 1.