Algebra and Trigonometry: Structure and Method, Book 2
Algebra and Trigonometry: Structure and Method, Book 2
2000th Edition
ISBN: 9780395977255
Author: MCDOUGAL LITTEL
Publisher: McDougal Littell
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Chapter 16.9, Problem 18WE
To determine

To prove: For the system of equations

  y=m1x+b1y=m2x+b2

Thecondition D=0 and Dy0 if and only if m1=m20 and b1b2 holds true.

Expert Solution & Answer
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Explanation of Solution

Given information:

The system of equations

  y=m1x+b1y=m2x+b2

Proof:

Consider system of equations

  y=m1x+b1y=m2x+b2

Write the above system in standard form,

  m1x+y=b1m2x+y=b2

The determinant of above system of equations is,

  D=|m11m21|=m1+m2

And,

  Dy=|m1b1m2b2|=b2m1+b1m2

If suppose D=0 and Dy0 then,

  m1+m2=0m1=m2

That is, m1=m20 for y=DyD to be valid.

And,

  b2m1+b1m20b1b2

Because m1=m2 .

Next suppose m1=m20 and b1b2 so,

  m1=m2m1+m2=0D=0

And,

  b1b2b2m1+b1m20Dy0

Hence, the condition D=0 and Dy0 if and only if m1=m20 and b1b2 holds true for given system of equations.

Chapter 16 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 16.1 - Prob. 11OECh. 16.1 - Prob. 12OECh. 16.1 - Prob. 13OECh. 16.1 - Prob. 14OECh. 16.1 - Prob. 15OECh. 16.1 - Prob. 16OECh. 16.1 - Prob. 17OECh. 16.1 - Prob. 18OECh. 16.1 - Prob. 1WECh. 16.1 - Prob. 2WECh. 16.1 - Prob. 3WECh. 16.1 - Prob. 4WECh. 16.1 - Prob. 5WECh. 16.1 - Prob. 6WECh. 16.1 - Prob. 7WECh. 16.1 - Prob. 8WECh. 16.1 - Prob. 9WECh. 16.1 - Prob. 10WECh. 16.1 - Prob. 11WECh. 16.1 - Prob. 12WECh. 16.1 - Prob. 13WECh. 16.1 - Prob. 14WECh. 16.1 - Prob. 15WECh. 16.1 - Prob. 16WECh. 16.1 - Prob. 17WECh. 16.1 - Prob. 18WECh. 16.1 - Prob. 19WECh. 16.1 - Prob. 20WECh. 16.1 - Prob. 21WECh. 16.1 - Prob. 22WECh. 16.1 - Prob. 1MRECh. 16.1 - Prob. 2MRECh. 16.1 - Prob. 3MRECh. 16.1 - Prob. 4MRECh. 16.1 - Prob. 5MRECh. 16.1 - Prob. 6MRECh. 16.1 - Prob. 7MRECh. 16.1 - Prob. 8MRECh. 16.2 - Prob. 1OECh. 16.2 - Prob. 2OECh. 16.2 - Prob. 3OECh. 16.2 - Prob. 4OECh. 16.2 - Prob. 5OECh. 16.2 - Prob. 6OECh. 16.2 - Prob. 7OECh. 16.2 - Prob. 8OECh. 16.2 - Prob. 9OECh. 16.2 - Prob. 10OECh. 16.2 - Prob. 11OECh. 16.2 - Prob. 12OECh. 16.2 - Prob. 13OECh. 16.2 - Prob. 1WECh. 16.2 - Prob. 2WECh. 16.2 - Prob. 3WECh. 16.2 - Prob. 4WECh. 16.2 - Prob. 5WECh. 16.2 - Prob. 6WECh. 16.2 - Prob. 7WECh. 16.2 - Prob. 8WECh. 16.2 - Prob. 9WECh. 16.2 - Prob. 10WECh. 16.2 - Prob. 11WECh. 16.2 - Prob. 12WECh. 16.2 - Prob. 13WECh. 16.2 - Prob. 14WECh. 16.2 - Prob. 15WECh. 16.2 - Prob. 16WECh. 16.2 - Prob. 17WECh. 16.2 - Prob. 18WECh. 16.2 - Prob. 19WECh. 16.2 - Prob. 20WECh. 16.2 - Prob. 21WECh. 16.2 - Prob. 22WECh. 16.2 - Prob. 23WECh. 16.2 - Prob. 24WECh. 16.2 - Prob. 25WECh. 16.2 - Prob. 26WECh. 16.2 - Prob. 27WECh. 16.2 - Prob. 28WECh. 16.3 - Prob. 1OECh. 16.3 - Prob. 2OECh. 16.3 - Prob. 3OECh. 16.3 - Prob. 4OECh. 16.3 - Prob. 5OECh. 16.3 - Prob. 6OECh. 16.3 - Prob. 7OECh. 16.3 - Prob. 8OECh. 16.3 - Prob. 9OECh. 16.3 - Prob. 10OECh. 16.3 - Prob. 11OECh. 16.3 - Prob. 12OECh. 16.3 - Prob. 13OECh. 16.3 - Prob. 14OECh. 16.3 - Prob. 15OECh. 16.3 - Prob. 16OECh. 16.3 - Prob. 1WECh. 16.3 - Prob. 2WECh. 16.3 - Prob. 3WECh. 16.3 - Prob. 4WECh. 16.3 - Prob. 5WECh. 16.3 - Prob. 6WECh. 16.3 - Prob. 7WECh. 16.3 - Prob. 8WECh. 16.3 - Prob. 9WECh. 16.3 - Prob. 10WECh. 16.3 - Prob. 11WECh. 16.3 - Prob. 12WECh. 16.3 - Prob. 13WECh. 16.3 - Prob. 14WECh. 16.3 - Prob. 15WECh. 16.3 - Prob. 16WECh. 16.3 - Prob. 17WECh. 16.3 - Prob. 18WECh. 16.3 - Prob. 19WECh. 16.3 - Prob. 20WECh. 16.3 - Prob. 21WECh. 16.3 - Prob. 22WECh. 16.3 - Prob. 23WECh. 16.3 - Prob. 24WECh. 16.3 - Prob. 25WECh. 16.3 - Prob. 26WECh. 16.3 - Prob. 27WECh. 16.3 - Prob. 28WECh. 16.3 - Prob. 29WECh. 16.3 - Prob. 30WECh. 16.3 - Prob. 1MRECh. 16.3 - Prob. 2MRECh. 16.3 - Prob. 3MRECh. 16.3 - Prob. 4MRECh. 16.3 - Prob. 5MRECh. 16.3 - Prob. 6MRECh. 16.3 - Prob. 7MRECh. 16.3 - Prob. 8MRECh. 16.3 - Prob. 9MRECh. 16.4 - Prob. 1OECh. 16.4 - Prob. 2OECh. 16.4 - Prob. 3OECh. 16.4 - Prob. 4OECh. 16.4 - Prob. 1WECh. 16.4 - Prob. 2WECh. 16.4 - Prob. 3WECh. 16.4 - Prob. 4WECh. 16.4 - Prob. 5WECh. 16.4 - Prob. 6WECh. 16.4 - Prob. 7WECh. 16.4 - Prob. 8WECh. 16.4 - Prob. 9WECh. 16.4 - Prob. 10WECh. 16.4 - Prob. 11WECh. 16.4 - Prob. 12WECh. 16.4 - Prob. 13WECh. 16.4 - Prob. 14WECh. 16.4 - Prob. 15WECh. 16.4 - Prob. 16WECh. 16.4 - Prob. 17WECh. 16.4 - Prob. 18WECh. 16.4 - Prob. 1STCh. 16.4 - Prob. 2STCh. 16.4 - Prob. 3STCh. 16.4 - Prob. 4STCh. 16.4 - Prob. 5STCh. 16.4 - Prob. 6STCh. 16.4 - Prob. 7STCh. 16.4 - Prob. 8STCh. 16.4 - Prob. 9STCh. 16.4 - Prob. 1ECh. 16.4 - Prob. 2ECh. 16.4 - Prob. 3ECh. 16.4 - Prob. 4ECh. 16.4 - Prob. 5ECh. 16.4 - Prob. 6ECh. 16.5 - Prob. 1OECh. 16.5 - Prob. 2OECh. 16.5 - Prob. 3OECh. 16.5 - Prob. 4OECh. 16.5 - Prob. 5OECh. 16.5 - Prob. 6OECh. 16.5 - Prob. 7OECh. 16.5 - Prob. 8OECh. 16.5 - Prob. 1WECh. 16.5 - Prob. 2WECh. 16.5 - Prob. 3WECh. 16.5 - Prob. 4WECh. 16.5 - Prob. 5WECh. 16.5 - Prob. 6WECh. 16.5 - Prob. 7WECh. 16.5 - Prob. 8WECh. 16.5 - Prob. 9WECh. 16.5 - Prob. 10WECh. 16.5 - Prob. 11WECh. 16.5 - Prob. 12WECh. 16.5 - Prob. 13WECh. 16.5 - Prob. 14WECh. 16.5 - Prob. 15WECh. 16.5 - Prob. 16WECh. 16.5 - Prob. 17WECh. 16.5 - Prob. 18WECh. 16.5 - Prob. 19WECh. 16.5 - Prob. 20WECh. 16.5 - Prob. 1MRECh. 16.5 - Prob. 2MRECh. 16.5 - Prob. 3MRECh. 16.5 - Prob. 4MRECh. 16.5 - Prob. 5MRECh. 16.5 - Prob. 6MRECh. 16.5 - Prob. 7MRECh. 16.5 - Prob. 8MRECh. 16.5 - Prob. 9MRECh. 16.6 - Prob. 1OECh. 16.6 - Prob. 2OECh. 16.6 - Prob. 3OECh. 16.6 - Prob. 4OECh. 16.6 - Prob. 5OECh. 16.6 - Prob. 6OECh. 16.6 - Prob. 7OECh. 16.6 - Prob. 8OECh. 16.6 - Prob. 9OECh. 16.6 - Prob. 10OECh. 16.6 - Prob. 11OECh. 16.6 - Prob. 12OECh. 16.6 - Prob. 13OECh. 16.6 - Prob. 1WECh. 16.6 - Prob. 2WECh. 16.6 - Prob. 3WECh. 16.6 - Prob. 4WECh. 16.6 - Prob. 5WECh. 16.6 - Prob. 6WECh. 16.6 - Prob. 7WECh. 16.6 - Prob. 8WECh. 16.6 - Prob. 9WECh. 16.6 - Prob. 10WECh. 16.6 - Prob. 11WECh. 16.6 - Prob. 12WECh. 16.6 - Prob. 13WECh. 16.6 - Prob. 14WECh. 16.6 - Prob. 15WECh. 16.6 - Prob. 16WECh. 16.6 - Prob. 17WECh. 16.6 - Prob. 18WECh. 16.6 - Prob. 19WECh. 16.6 - Prob. 20WECh. 16.6 - Prob. 1STCh. 16.6 - Prob. 2STCh. 16.6 - Prob. 3STCh. 16.6 - Prob. 4STCh. 16.7 - Prob. 1OECh. 16.7 - Prob. 2OECh. 16.7 - Prob. 3OECh. 16.7 - Prob. 4OECh. 16.7 - Prob. 5OECh. 16.7 - Prob. 6OECh. 16.7 - Prob. 1WECh. 16.7 - Prob. 2WECh. 16.7 - Prob. 3WECh. 16.7 - Prob. 4WECh. 16.7 - Prob. 5WECh. 16.7 - Prob. 6WECh. 16.7 - Prob. 7WECh. 16.7 - Prob. 8WECh. 16.7 - Prob. 9WECh. 16.7 - Prob. 10WECh. 16.7 - Prob. 11WECh. 16.7 - Prob. 12WECh. 16.7 - Prob. 13WECh. 16.7 - Prob. 14WECh. 16.7 - Prob. 15WECh. 16.7 - Prob. 16WECh. 16.7 - Prob. 17WECh. 16.7 - Prob. 18WECh. 16.7 - Prob. 19WECh. 16.7 - Prob. 1MRECh. 16.7 - Prob. 2MRECh. 16.7 - Prob. 3MRECh. 16.7 - Prob. 4MRECh. 16.7 - Prob. 5MRECh. 16.7 - Prob. 6MRECh. 16.8 - Prob. 1OECh. 16.8 - Prob. 2OECh. 16.8 - Prob. 3OECh. 16.8 - Prob. 4OECh. 16.8 - Prob. 1WECh. 16.8 - Prob. 2WECh. 16.8 - Prob. 3WECh. 16.8 - Prob. 4WECh. 16.8 - Prob. 5WECh. 16.8 - Prob. 6WECh. 16.8 - Prob. 7WECh. 16.8 - Prob. 8WECh. 16.8 - Prob. 9WECh. 16.8 - Prob. 10WECh. 16.8 - Prob. 11WECh. 16.8 - Prob. 12WECh. 16.8 - Prob. 13WECh. 16.8 - Prob. 14WECh. 16.8 - Prob. 15WECh. 16.9 - Prob. 1OECh. 16.9 - Prob. 2OECh. 16.9 - Prob. 3OECh. 16.9 - Prob. 4OECh. 16.9 - Prob. 5OECh. 16.9 - Prob. 6OECh. 16.9 - Prob. 7OECh. 16.9 - Prob. 8OECh. 16.9 - Prob. 9OECh. 16.9 - Prob. 10OECh. 16.9 - Prob. 11OECh. 16.9 - Prob. 12OECh. 16.9 - Prob. 13OECh. 16.9 - Prob. 14OECh. 16.9 - Prob. 15OECh. 16.9 - Prob. 16OECh. 16.9 - Prob. 1WECh. 16.9 - Prob. 2WECh. 16.9 - Prob. 3WECh. 16.9 - Prob. 4WECh. 16.9 - Prob. 5WECh. 16.9 - Prob. 6WECh. 16.9 - Prob. 7WECh. 16.9 - Prob. 8WECh. 16.9 - Prob. 9WECh. 16.9 - Prob. 10WECh. 16.9 - Prob. 11WECh. 16.9 - Prob. 12WECh. 16.9 - Prob. 13WECh. 16.9 - Prob. 14WECh. 16.9 - Prob. 15WECh. 16.9 - Prob. 16WECh. 16.9 - Prob. 17WECh. 16.9 - Prob. 18WECh. 16.9 - Prob. 19WECh. 16.9 - Prob. 1MRECh. 16.9 - Prob. 2MRECh. 16.9 - Prob. 3MRECh. 16.9 - Prob. 4MRECh. 16.9 - Prob. 5MRECh. 16.9 - Prob. 6MRECh. 16.9 - Prob. 7MRECh. 16.9 - Prob. 1STCh. 16.9 - Prob. 2STCh. 16.9 - Prob. 3STCh. 16 - Prob. 1CRCh. 16 - Prob. 2CRCh. 16 - Prob. 3CRCh. 16 - Prob. 4CRCh. 16 - Prob. 5CRCh. 16 - Prob. 6CRCh. 16 - Prob. 7CRCh. 16 - Prob. 8CRCh. 16 - Prob. 9CRCh. 16 - Prob. 10CRCh. 16 - Prob. 1CTCh. 16 - Prob. 2CTCh. 16 - Prob. 3CTCh. 16 - Prob. 4CTCh. 16 - Prob. 5CTCh. 16 - Prob. 6CTCh. 16 - Prob. 7CTCh. 16 - Prob. 8CTCh. 16 - Prob. 9CTCh. 16 - Prob. 10CTCh. 16 - Prob. 11CTCh. 16 - Prob. 12CTCh. 16 - Prob. 13CTCh. 16 - Prob. 14CTCh. 16 - Prob. 15CT
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