## Algebra 1

Published by Prentice Hall

# Chapter 12 - Data Analysis and Probability - 12-1 Organizing Data Using Matrices - Practice and Problem-Solving Exercises - Page 719: 32

#### Answer

#1 x - 3y = 7 3x + 2y = 10 #2 x - 3y = 7 + 3y , +3y x = 7 + 3y #3 3x + 2y = 10 3 \times (7 + 3y) + 2y = 10 #4 (3\times 7) + (3\times 3y) + 2y = 10 21 + 9y + 2y = 10 -21 , , , , , , , , , -21 9y + 2y = -11 11y = -11 11y\div11 = -11\div11 y = -1 #5 x = 7 + 3\times(-1) x = 7 - 3 x = 4 #6 x = 4 , y = -1

#### Work Step by Step

#1 In order for the equation to be true the corresponding numbers in the first two matrices added together must equal the corresponding number in the final matrix (top left of first plus top left of second equals top left of final) #2 solve one equation for x (keep in mind you could solve either equation for either variable to start) #3 substitute the equation for x into the other equation. #4 solve for y #5 now that you know y substitute it in to either equation to find x #6 The values of x and y

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