<< Chapter < Page Chapter >> Page >
<para>This module is from<link document="col10614">Elementary Algebra</link>by Denny Burzynski and Wade Ellis, Jr.</para>This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. In this chapter, the emphasis is on the mechanics of equation solving, which clearly explains how to isolate a variable. The goal is to help the student feel more comfortable with solving applied problems. Ample opportunity is provided for the student to practice translating words to symbols, which is an important part of the "Five-Step Method" of solving applied problems (discussed in modules (<link document="m21980"/>) and (<link document="m21979"/>)). Objectives of this module: be able to identify the solution of a linear equation in two variables, know that solutions to linear equations in two variables can be written as ordered pairs.

Overview

  • Solutions to Linear Equations in Two Variables
  • Ordered Pairs as Solutions

Solutions to linear equations in two variables

Solution to an equation in two variables

We have discovered that an equation is a mathematical way of expressing the relationship of equality between quantities. If the relationship is between two quantities, the equation will contain two variables. We say that an equation in two variables has a solution if an ordered pair of values can be found such that when these two values are substituted into the equation a true statement results. This is illustrated when we observe some solutions to the equation y = 2 x + 5 .

  1. x = 4 , y = 13 ; since 13 = 2 ( 4 ) + 5 is true .
  2. x = 1 , y = 7 ; since 7 = 2 ( 1 ) + 5 is true .
  3. x = 0 , y = 5 ; since 5 = 2 ( 0 ) + 5 is true .
  4. x = 6 , y = 7 ; since -7 = 2 ( 6 ) + 5 is true .

Ordered pairs as solutions

It is important to keep in mind that a solution to a linear equation in two variables is an ordered pair of values, one value for each variable. A solution is not completely known until the values of both variables are specified.

Independent and dependent variables

Recall that, in an equation, any variable whose value can be freely assigned is said to be an independent variable. Any variable whose value is determined once the other value or values have been assigned is said to be a dependent variable. If, in a linear equation, the independent variable is x and the dependent variable is y , and a solution to the equation is x = a and y = b , the solution is written as the

ORDERED PAIR      ( a , b )

Ordered pair

In an ordered pair , ( a , b ) , the first component, a , gives the value of the independent variable, and the second component, b , gives the value of the dependent variable.

In an ordered pair (a,b), the first component a is the value of the independent variable, and the second component b is the value of the dependent variable.

We can use ordered pairs to show some solutions to the equation y = 6 x 7 .

( 0 , 7 ) .
If x = 0 and y = 7 , we get a true statement upon substitution and computataion.

y = 6 x 7 7 = 6 ( 0 ) 7 Is this correct? 7 = 7 Yes, this is correct .

Got questions? Get instant answers now!

( 8 , 41 ) .
If x = 8 and y = 41 , we get a true statement upon substitution and computataion.

y = 6 x 7 41 = 6 ( 8 ) 7 Is this correct? 41 = 48 7 Is this correct? 41 = 41 Yes, this is correct .

Got questions? Get instant answers now!

( 4 , 31 ) .
If x = 4 and y = 31 , we get a true statement upon substitution and computataion.

y = 6 x 7 31 = 6 ( 4 ) 7 Is this correct? 31 = 24 7 Is this correct? 31 = 31 Yes, this is correct .

Got questions? Get instant answers now!

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask