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2. Allison and Emily were asked to solve this system of three linear equations using substitution. Analyze their methods. X+y+z = -2 2x - 3y + 2z = -14 4x +3y -z = 5

2. Allison and Emily were asked to solve this system of three linear equations using substitution. Analyze their methods. X+y+z = -2 2x - 3y + 2z = -14 4x +3y -z = 5

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Systems Of Linear Equations
Section1.2: Guassian Eliminationa And Guass-jordan Elimination
Problem 53E
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2. Allison and Emily were asked to solve this system of three linear equations using substitution. Analyze their methods. x+y+z =-2 2x - 3y + 2z = -14 4x +3y-z 5 Allison x + y + z = -2 X = -2 - y - 2 2x - 3y + 2z = -14 4x + 3y - z = 5 4(-2 - y- z) + 3y - z = 5 -8 - 4y - 4z + 3y – z = 5 2(-2 - y - z) 3y + 2z = -14 -4 - 2y - 2z - 3y + 2z = -14 -4 - 5y = -14 -8 - y - 5z = 5 y + 5z = -13 -5y = -10 Then I solved -5y = -10 the system y + 5z = -13 · Emilų 4x + 3y - 2 = 5 4x + 34 - 5 = 2 2x - 3y + 2z = -14 x + y + 2 = -2 x + 4 + (4x + 34 -5) = -2 2x - 34 + 2(4x + 3y-5) = -14 2x - 3y + 8x + by - 10 = -14 Sx + 4y -5 = -2 10x + 3y - 10 = -14 Sx + 44 = 3 10x + 3y = -4 Then I solved the system 10x + 3y = -4 Sx + 4y = 3 18
Transcribed Image Text:2. Allison and Emily were asked to solve this system of three linear equations using substitution. Analyze their methods. x+y+z =-2 2x - 3y + 2z = -14 4x +3y-z 5 Allison x + y + z = -2 X = -2 - y - 2 2x - 3y + 2z = -14 4x + 3y - z = 5 4(-2 - y- z) + 3y - z = 5 -8 - 4y - 4z + 3y – z = 5 2(-2 - y - z) 3y + 2z = -14 -4 - 2y - 2z - 3y + 2z = -14 -4 - 5y = -14 -8 - y - 5z = 5 y + 5z = -13 -5y = -10 Then I solved -5y = -10 the system y + 5z = -13 · Emilų 4x + 3y - 2 = 5 4x + 34 - 5 = 2 2x - 3y + 2z = -14 x + y + 2 = -2 x + 4 + (4x + 34 -5) = -2 2x - 34 + 2(4x + 3y-5) = -14 2x - 3y + 8x + by - 10 = -14 Sx + 4y -5 = -2 10x + 3y - 10 = -14 Sx + 44 = 3 10x + 3y = -4 Then I solved the system 10x + 3y = -4 Sx + 4y = 3 18
a. Describe the similarities and differences in Allison's and Emily's methods. b. Demonstrate that Allison's method and Emily's method will both yield the same solution. Explain your reasoning. c. Could this system have been solved using a different substitution? How do you select which variable to solve for? Explain your reasoning. 3. During the movie fundraising event, the concession stand at the auditorium sells popcorn, fruit, and drinks. The price of a box of popcorn is $0.50 more than the price of a piece of fruit, and the price of two drinks is $0.50 less than the price of three pieces of fruit. You order two boxes of popcorn, one piece of fruit, and three drinks, and the total comes to $7.75. a. Write a system of three linear equations in three variables to represent this situation. Be sure to define your variables. b. Calculate the price of each item. Use substitution to solve the system of three linear equations in three variables.
Transcribed Image Text:a. Describe the similarities and differences in Allison's and Emily's methods. b. Demonstrate that Allison's method and Emily's method will both yield the same solution. Explain your reasoning. c. Could this system have been solved using a different substitution? How do you select which variable to solve for? Explain your reasoning. 3. During the movie fundraising event, the concession stand at the auditorium sells popcorn, fruit, and drinks. The price of a box of popcorn is $0.50 more than the price of a piece of fruit, and the price of two drinks is $0.50 less than the price of three pieces of fruit. You order two boxes of popcorn, one piece of fruit, and three drinks, and the total comes to $7.75. a. Write a system of three linear equations in three variables to represent this situation. Be sure to define your variables. b. Calculate the price of each item. Use substitution to solve the system of three linear equations in three variables.
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