a. Answer There will be infinitely many solutions and one of the solution is x = 0 and y = − 5 Explanation Given information: The given equations are, y = 2 3 x − 5 4 x − 6 y = 30 The equation can also be written as: y = 2 3 x − 5 3 y = 2 x − 15 3 y − 2 x = − 15 4 x − 6 y = 30 2 x − 3 y = 15 Consider the graph of the given equations, Since, the graph of the two lines are coincident on each other Thus, there will be infinitely many solutions and one of the solutions is x = 0 and y = − 5 b. To determine To find: The solution of the given equations by using substitution method. Answer Thus, the given equations have infinitely many solutions. Explanation Given information: The given equations are, y = 2 3 x − 5 4 x − 6 y = 30 The given equation can be written as, y = 2 3 x − 5 The another given equation is, 4 x − 6 y = 30 2 x − 3 y = 15 Substitute 2 3 x − 5 for y . 2 x − 3 ( 2 3 x − 5 ) = 15 2 x − 3 ( 2 x − 15 3 ) = 15 2 x − 2 x + 15 = 15 15 = 15 0 = 0 Thus, the given equations have infinitely many solutions.

(REV)00 Edition

ISBN: 9780395977224

Author: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher: McDougal Littell

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Question

Chapter 9.2, Problem 35WE

To determine

To find: The solution of the given equations by using graphing method.

Expert Solution

Answer to Problem 35WE

There will be infinitely many solutions and one of the solution is x=0 and y=−5

Explanation of Solution

Given information:

The given equations are,

y=23x−54x−6y=30

The equation can also be written as:

y=23x−53y=2x−153y−2x=−15

4x−6y=302x−3y=15

Consider the graph of the given equations,

Algebra: Structure And Method, Book 1, Chapter 9.2, Problem 35WE

Since, the graph of the two lines are coincident on each other

Thus, there will be infinitely many solutions and one of the solutions is x=0 and y=−5

To determine

To find: The solution of the given equations by using substitution method.

Expert Solution

Answer to Problem 35WE

Thus, the given equations have infinitely many solutions.

Explanation of Solution

Given information:

The given equations are,

y=23x−54x−6y=30

The given equation can be written as,

y=23x−5

The another given equation is,

4x−6y=302x−3y=15

Substitute 23x−5 for y .

2x−3(23x−5)=152x−3(2x−153)=152x−2x+15=1515=150=0

Thus, the given equations have infinitely many solutions.

Chapter 9.2, Problem 34WE

Chapter 9.2, Problem 36WE

Chapter 9 Solutions

Algebra: Structure And Method, Book 1

Ch. 9.1 - Prob. 1OE Ch. 9.1 - Prob. 2OE Ch. 9.1 - Prob. 3OE Ch. 9.1 - Prob. 4OE Ch. 9.1 - Prob. 5OE Ch. 9.1 - Prob. 6OE Ch. 9.1 - Prob. 7OE Ch. 9.1 - Prob. 8OE Ch. 9.1 - Prob. 9OE Ch. 9.1 - Prob. 1WE

Ch. 9.1 - Prob. 2WE Ch. 9.1 - Prob. 3WE Ch. 9.1 - Prob. 4WE Ch. 9.1 - Prob. 5WE Ch. 9.1 - Prob. 6WE Ch. 9.1 - Prob. 7WE Ch. 9.1 - Prob. 8WE Ch. 9.1 - Prob. 9WE Ch. 9.1 - Prob. 10WE Ch. 9.1 - Prob. 11WE Ch. 9.1 - Prob. 12WE Ch. 9.1 - Prob. 13WE Ch. 9.1 - Prob. 14WE Ch. 9.1 - Prob. 15WE Ch. 9.1 - Prob. 16WE Ch. 9.1 - Prob. 17WE Ch. 9.1 - Prob. 18WE Ch. 9.1 - Prob. 19WE Ch. 9.1 - Prob. 20WE Ch. 9.1 - Prob. 21WE Ch. 9.1 - Prob. 22WE Ch. 9.1 - Prob. 23WE Ch. 9.1 - Prob. 24WE Ch. 9.1 - Prob. 1MRE Ch. 9.1 - Prob. 2MRE Ch. 9.1 - Prob. 3MRE Ch. 9.1 - Prob. 4MRE Ch. 9.1 - Prob. 5MRE Ch. 9.1 - Prob. 6MRE Ch. 9.1 - Prob. 1CE Ch. 9.1 - Prob. 2CE Ch. 9.1 - Prob. 3CE Ch. 9.1 - Prob. 4CE Ch. 9.2 - Prob. 1OE Ch. 9.2 - Prob. 2OE Ch. 9.2 - Prob. 3OE Ch. 9.2 - Prob. 4OE Ch. 9.2 - Prob. 5OE Ch. 9.2 - Prob. 6OE Ch. 9.2 - Prob. 7OE Ch. 9.2 - Prob. 8OE Ch. 9.2 - Prob. 9OE Ch. 9.2 - Prob. 10OE Ch. 9.2 - Prob. 11OE Ch. 9.2 - Prob. 12OE Ch. 9.2 - Prob. 1WE Ch. 9.2 - Prob. 2WE Ch. 9.2 - Prob. 3WE Ch. 9.2 - Prob. 4WE Ch. 9.2 - Prob. 5WE Ch. 9.2 - Prob. 6WE Ch. 9.2 - Prob. 7WE Ch. 9.2 - Prob. 8WE Ch. 9.2 - Prob. 9WE Ch. 9.2 - Prob. 10WE Ch. 9.2 - Prob. 11WE Ch. 9.2 - Prob. 12WE Ch. 9.2 - Prob. 13WE Ch. 9.2 - Prob. 14WE Ch. 9.2 - Prob. 15WE Ch. 9.2 - Prob. 16WE Ch. 9.2 - Prob. 17WE Ch. 9.2 - Prob. 18WE Ch. 9.2 - Prob. 19WE Ch. 9.2 - Prob. 20WE Ch. 9.2 - Prob. 21WE Ch. 9.2 - Prob. 22WE Ch. 9.2 - Prob. 23WE Ch. 9.2 - Prob. 24WE Ch. 9.2 - Prob. 25WE Ch. 9.2 - Prob. 26WE Ch. 9.2 - Prob. 27WE Ch. 9.2 - Prob. 28WE Ch. 9.2 - Prob. 29WE Ch. 9.2 - Prob. 30WE Ch. 9.2 - Prob. 31WE Ch. 9.2 - Prob. 32WE Ch. 9.2 - Prob. 33WE Ch. 9.2 - Prob. 34WE Ch. 9.2 - Prob. 35WE Ch. 9.2 - Prob. 36WE Ch. 9.2 - Prob. 37WE Ch. 9.2 - Prob. 38WE Ch. 9.2 - Prob. 39WE Ch. 9.2 - Prob. 40WE Ch. 9.2 - Prob. 41WE Ch. 9.2 - Prob. 1MRE Ch. 9.2 - Prob. 2MRE Ch. 9.2 - Prob. 3MRE Ch. 9.2 - Prob. 4MRE Ch. 9.2 - Prob. 5MRE Ch. 9.2 - Prob. 6MRE Ch. 9.2 - Prob. 7MRE Ch. 9.2 - Prob. 8MRE Ch. 9.2 - Prob. 9MRE Ch. 9.2 - Prob. 10MRE Ch. 9.2 - Prob. 11MRE Ch. 9.2 - 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