Solve the following pair of simultaneous equations for x and y.

ax+y=c

x+by=d

I don't know why I can't get this one, because it seems pretty simple.

So far I've done this:

I multiplied 1 and 2 and got abx+by=cb

Then I added that and 2 together and got abx+x+2by=cd+d

x(ab+1)+2by=cd+d

(cb+d)/(ab+1)=x+2by

(cd+d)/(ab+1)-2by=x

However the answer in the back of the book is: x=(d-bc)/(1-ab).

I'm just not too sure where I went wrong.

Thanks.