# Chapter 8 - Coordinate Geometry and Linear Systems - 8.6 - Elimination-by-Addition Method - Problem Set 8.6 - Page 378: 47

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: $x + 21 = 35 \\ x =14$

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