#### Answer

14 books for 22 dollars and 21 books for 34 dollars

#### Work Step by Step

We call x the books for 22 dollars and y the books for 34 dollars. Thus, we obtain:
$ x + y = 35 $
And
$ 22x +34y =1022$
In order to solve this problem, we multiply one or both of the equations by a value that will make one of the variables cancel. We multiply the top equation by -22, and we multiply the bottom equation by 1. Then, we add the two equations to obtain:
$12y = 252 \\ y = 21 $
We plug in the given value into the top equation and solve for the other variable:
$ x + 21 = 35 \\ x =14$