## Elementary Algebra

Published by Cengage Learning

# Chapter 8 - Coordinate Geometry and Linear Systems - 8.6 - Elimination-by-Addition Method - Problem Set 8.6 - Page 378: 51

#### Answer

6 dollars for cheese pizza and 8 dollars for pepperoni pizza.

#### Work Step by Step

We call x the cost of cheese pizzas and y the cost of pepperoni pizza. Thus, we obtain: $5x +12y =126$ And $9x +20y = 214$ 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 -9, and we multiply the bottom equation by 5. Then, we add the two equations to obtain: $-8y = -64 \\ y =8$ We plug in the given value into the top equation and solve for the other variable: $5x + 12(8) = 126 \\ 5x = 30 \\ x =6$

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