SlideShare a Scribd company logo
1 of 14
System of equations
A pair of linear equations in two variables is
said to form a system of simultaneous linear
equations.
For Example, 2x – 3y + 4 = 0
x + 7y – 1 = 0
Form a system of two linear equations in
variables x and y.
The general form of a linear equation in two
variables x and y is
ax + by + c = 0 , a and b is not equal to
zero, where
a, b and c being real numbers.
A solution of such an equation is a pair of
values, One for x and the other for y, Which
makes two sides of the equation equal.
Every linear equation in two variables has
infinitely many solutions which can be
represented on a certain line.
GRAPHICAL SOLUTIONS OF A
LINEAR EQUATION
Let us consider the following system of two
simultaneous linear equations in two
variable.
2x – y = -1
3x + 2y = 9
Here we assign any value to one of the two
variables and then determine the value of
the other variable from the given equation.
For the equation
2x –y = -1 ---(1)
2x +1 = y
Y = 2x + 1
3x + 2y = 9 --- (2)
2y = 9 – 3x
Y = 9-3x
X 0 2
Y 1 5
X 3 -1
Y 0 6
XX
Y
Y
(2,5)
(-1,6)
(0,3)(0,1)
X= 1
Y=3
Let us take an example
x + 2y = -1 ------------------ (i)
2x – 3y = 12 -----------------(ii)
SUBSTITUTION METHOD
x + 2y = -1
x = -2y -1 ------- (iii)
Substituting the value of x in
equation (ii), we get
2x – 3y = 12
2 ( -2y – 1) – 3y = 12
- 4y – 2 – 3y = 12
- 7y = 14 , y = -2 ,
SUBSTITUTION
Putting the value of y in eq. (iii), we get
x = - 2y -1
x = - 2 x (-2) – 1
= 4 – 1
= 3
Hence the solution of the equation is
( 3, - 2 )
ELIMINATION METHOD
• In this method, we eliminate one of the
two variables to obtain an equation in one
variable which can easily be solved.
Putting the value of this variable in any of
the given equations, The value of the
other variable can be obtained.
• For example: we want to solve,
3x + 2y = 11
2x + 3y = 4
Let 3x + 2y = 11 --------- (i)
2x + 3y = 4 ---------(ii)
Multiply 3 in equation (i) and 2 in equation (ii) and
subtracting eq. iv from iii, we get
9x + 6y = 33 ------ (iii)
4x + 6y = 8 ------- (iv)
5x = 25
x = 5
• putting the value of y in equation (ii) we get,
2x + 3y = 4
2 x 5 + 3y = 4
10 + 3y = 4
3y = 4 – 10
3y = - 6
y = - 2
Hence, x = 5 and y = -2
Maths ppt   linear equations in two variables
Maths ppt   linear equations in two variables

More Related Content

What's hot

CLASS 9 LINEAR EQUATIONS IN TWO VARIABLES PPT
CLASS 9 LINEAR EQUATIONS IN TWO VARIABLES PPTCLASS 9 LINEAR EQUATIONS IN TWO VARIABLES PPT
CLASS 9 LINEAR EQUATIONS IN TWO VARIABLES PPT05092000
 
Linear equation in two variables
Linear equation in two variablesLinear equation in two variables
Linear equation in two variablesMERBGOI
 
Pair Of Linear Equations In Two Variables
Pair Of Linear Equations In Two VariablesPair Of Linear Equations In Two Variables
Pair Of Linear Equations In Two VariablesDeo Baran
 
PPT on Linear Equations in two variables
PPT on Linear Equations in two variables PPT on Linear Equations in two variables
PPT on Linear Equations in two variables sagar9971
 
Graphing Quadratic Functions in Standard Form
Graphing Quadratic Functions in Standard FormGraphing Quadratic Functions in Standard Form
Graphing Quadratic Functions in Standard Formcmorgancavo
 
Direct and inverse proportion
Direct and inverse proportionDirect and inverse proportion
Direct and inverse proportionAnkit Goel
 
Algebra PPT
Algebra PPTAlgebra PPT
Algebra PPTsri_3007
 
Linear equation in two variable
Linear equation in two variableLinear equation in two variable
Linear equation in two variableRamjas College
 
3 2 solving systems of equations (elimination method)
3 2 solving systems of equations (elimination method)3 2 solving systems of equations (elimination method)
3 2 solving systems of equations (elimination method)Hazel Joy Chong
 
Finding Slope Given A Graph And Two Points
Finding Slope Given A Graph And Two PointsFinding Slope Given A Graph And Two Points
Finding Slope Given A Graph And Two PointsGillian Guiang
 
Quadratic equation slideshare
Quadratic equation slideshareQuadratic equation slideshare
Quadratic equation slideshareAnusharani771
 
LINEAR EQUATION IN TWO VARIABLES
LINEAR EQUATION IN TWO VARIABLESLINEAR EQUATION IN TWO VARIABLES
LINEAR EQUATION IN TWO VARIABLESManah Chhabra
 
Pairs of linear equation in two variable by asim rajiv shandilya 10th a
Pairs of linear equation in two variable by asim rajiv shandilya 10th aPairs of linear equation in two variable by asim rajiv shandilya 10th a
Pairs of linear equation in two variable by asim rajiv shandilya 10th aasim1001
 
Solving Systems by Substitution
Solving Systems by SubstitutionSolving Systems by Substitution
Solving Systems by Substitutionswartzje
 
Substitution Method of Systems of Linear Equations
Substitution Method of Systems of Linear EquationsSubstitution Method of Systems of Linear Equations
Substitution Method of Systems of Linear EquationsSonarin Cruz
 
Quadratic equations class 10
Quadratic equations class 10Quadratic equations class 10
Quadratic equations class 10AadhiSXA
 
Linear Equation in one variable - Class 8 th Maths
Linear Equation in one variable - Class 8 th MathsLinear Equation in one variable - Class 8 th Maths
Linear Equation in one variable - Class 8 th MathsAmit Choube
 

What's hot (20)

CLASS 9 LINEAR EQUATIONS IN TWO VARIABLES PPT
CLASS 9 LINEAR EQUATIONS IN TWO VARIABLES PPTCLASS 9 LINEAR EQUATIONS IN TWO VARIABLES PPT
CLASS 9 LINEAR EQUATIONS IN TWO VARIABLES PPT
 
Chapter 5 Slope-Intercept Form
Chapter 5 Slope-Intercept FormChapter 5 Slope-Intercept Form
Chapter 5 Slope-Intercept Form
 
Linear equation in two variables
Linear equation in two variablesLinear equation in two variables
Linear equation in two variables
 
Pair Of Linear Equations In Two Variables
Pair Of Linear Equations In Two VariablesPair Of Linear Equations In Two Variables
Pair Of Linear Equations In Two Variables
 
PPT on Linear Equations in two variables
PPT on Linear Equations in two variables PPT on Linear Equations in two variables
PPT on Linear Equations in two variables
 
Graphing Quadratic Functions in Standard Form
Graphing Quadratic Functions in Standard FormGraphing Quadratic Functions in Standard Form
Graphing Quadratic Functions in Standard Form
 
Direct and inverse proportion
Direct and inverse proportionDirect and inverse proportion
Direct and inverse proportion
 
Polynomials
PolynomialsPolynomials
Polynomials
 
Polynomials
PolynomialsPolynomials
Polynomials
 
Algebra PPT
Algebra PPTAlgebra PPT
Algebra PPT
 
Linear equation in two variable
Linear equation in two variableLinear equation in two variable
Linear equation in two variable
 
3 2 solving systems of equations (elimination method)
3 2 solving systems of equations (elimination method)3 2 solving systems of equations (elimination method)
3 2 solving systems of equations (elimination method)
 
Finding Slope Given A Graph And Two Points
Finding Slope Given A Graph And Two PointsFinding Slope Given A Graph And Two Points
Finding Slope Given A Graph And Two Points
 
Quadratic equation slideshare
Quadratic equation slideshareQuadratic equation slideshare
Quadratic equation slideshare
 
LINEAR EQUATION IN TWO VARIABLES
LINEAR EQUATION IN TWO VARIABLESLINEAR EQUATION IN TWO VARIABLES
LINEAR EQUATION IN TWO VARIABLES
 
Pairs of linear equation in two variable by asim rajiv shandilya 10th a
Pairs of linear equation in two variable by asim rajiv shandilya 10th aPairs of linear equation in two variable by asim rajiv shandilya 10th a
Pairs of linear equation in two variable by asim rajiv shandilya 10th a
 
Solving Systems by Substitution
Solving Systems by SubstitutionSolving Systems by Substitution
Solving Systems by Substitution
 
Substitution Method of Systems of Linear Equations
Substitution Method of Systems of Linear EquationsSubstitution Method of Systems of Linear Equations
Substitution Method of Systems of Linear Equations
 
Quadratic equations class 10
Quadratic equations class 10Quadratic equations class 10
Quadratic equations class 10
 
Linear Equation in one variable - Class 8 th Maths
Linear Equation in one variable - Class 8 th MathsLinear Equation in one variable - Class 8 th Maths
Linear Equation in one variable - Class 8 th Maths
 

Viewers also liked

Elimination method Ch 7
Elimination method Ch 7Elimination method Ch 7
Elimination method Ch 7Wood-Ridge
 
Evaluating Algebraic Expressions
Evaluating Algebraic ExpressionsEvaluating Algebraic Expressions
Evaluating Algebraic Expressionsbizarregirl
 
Lesson Plan in Math II
Lesson Plan in Math IILesson Plan in Math II
Lesson Plan in Math IIjanehbasto
 
Lesson plan in English 1
Lesson plan in English 1Lesson plan in English 1
Lesson plan in English 1janehbasto
 
Lesson Plan i Mathematics
Lesson Plan i MathematicsLesson Plan i Mathematics
Lesson Plan i Mathematicsjanehbasto
 
Helen of Troy PLot CHaracters and Conflict
Helen of Troy PLot CHaracters and ConflictHelen of Troy PLot CHaracters and Conflict
Helen of Troy PLot CHaracters and Conflictjanehbasto
 
Variables & Expressions
Variables & ExpressionsVariables & Expressions
Variables & Expressionsrfant
 
Biological Basis of Personality
Biological Basis of PersonalityBiological Basis of Personality
Biological Basis of Personalityjanehbasto
 
Detailed Lesson Plan in Arts for Primary Level
Detailed Lesson Plan in Arts for Primary LevelDetailed Lesson Plan in Arts for Primary Level
Detailed Lesson Plan in Arts for Primary Leveljanehbasto
 
Detailed Lesson plan of Product Rule for Exponent Using the Deductive Method
Detailed Lesson plan of Product Rule for Exponent Using the Deductive MethodDetailed Lesson plan of Product Rule for Exponent Using the Deductive Method
Detailed Lesson plan of Product Rule for Exponent Using the Deductive MethodLorie Jane Letada
 
Lessonplan 100512115922-phpapp02 (1)
Lessonplan 100512115922-phpapp02 (1)Lessonplan 100512115922-phpapp02 (1)
Lessonplan 100512115922-phpapp02 (1)Fender Zildjian
 
Algebra Foundations Series- 1.1 Variables and Expressions
Algebra Foundations Series- 1.1 Variables and ExpressionsAlgebra Foundations Series- 1.1 Variables and Expressions
Algebra Foundations Series- 1.1 Variables and ExpressionsDee Black
 
1.6 Algebra and Angles
1.6 Algebra and Angles1.6 Algebra and Angles
1.6 Algebra and AnglesDee Black
 
Detailed lesson plan in elementary algebra
Detailed lesson plan in elementary algebraDetailed lesson plan in elementary algebra
Detailed lesson plan in elementary algebrajennilynbalbalosa
 

Viewers also liked (20)

8. lesson plan 2.1 lestv
8. lesson plan 2.1 lestv8. lesson plan 2.1 lestv
8. lesson plan 2.1 lestv
 
Mathematics
MathematicsMathematics
Mathematics
 
Translating Expressions
Translating ExpressionsTranslating Expressions
Translating Expressions
 
Elimination method Ch 7
Elimination method Ch 7Elimination method Ch 7
Elimination method Ch 7
 
Class8
Class8Class8
Class8
 
Evaluating Algebraic Expressions
Evaluating Algebraic ExpressionsEvaluating Algebraic Expressions
Evaluating Algebraic Expressions
 
Lesson Plan in Math II
Lesson Plan in Math IILesson Plan in Math II
Lesson Plan in Math II
 
Lesson plan in English 1
Lesson plan in English 1Lesson plan in English 1
Lesson plan in English 1
 
Lesson Plan i Mathematics
Lesson Plan i MathematicsLesson Plan i Mathematics
Lesson Plan i Mathematics
 
Helen of Troy PLot CHaracters and Conflict
Helen of Troy PLot CHaracters and ConflictHelen of Troy PLot CHaracters and Conflict
Helen of Troy PLot CHaracters and Conflict
 
Variables & Expressions
Variables & ExpressionsVariables & Expressions
Variables & Expressions
 
Biological Basis of Personality
Biological Basis of PersonalityBiological Basis of Personality
Biological Basis of Personality
 
Lp arts
Lp artsLp arts
Lp arts
 
Detailed Lesson Plan in Arts for Primary Level
Detailed Lesson Plan in Arts for Primary LevelDetailed Lesson Plan in Arts for Primary Level
Detailed Lesson Plan in Arts for Primary Level
 
Algebraic expression
Algebraic expressionAlgebraic expression
Algebraic expression
 
Detailed Lesson plan of Product Rule for Exponent Using the Deductive Method
Detailed Lesson plan of Product Rule for Exponent Using the Deductive MethodDetailed Lesson plan of Product Rule for Exponent Using the Deductive Method
Detailed Lesson plan of Product Rule for Exponent Using the Deductive Method
 
Lessonplan 100512115922-phpapp02 (1)
Lessonplan 100512115922-phpapp02 (1)Lessonplan 100512115922-phpapp02 (1)
Lessonplan 100512115922-phpapp02 (1)
 
Algebra Foundations Series- 1.1 Variables and Expressions
Algebra Foundations Series- 1.1 Variables and ExpressionsAlgebra Foundations Series- 1.1 Variables and Expressions
Algebra Foundations Series- 1.1 Variables and Expressions
 
1.6 Algebra and Angles
1.6 Algebra and Angles1.6 Algebra and Angles
1.6 Algebra and Angles
 
Detailed lesson plan in elementary algebra
Detailed lesson plan in elementary algebraDetailed lesson plan in elementary algebra
Detailed lesson plan in elementary algebra
 

Similar to Maths ppt linear equations in two variables

Linear equation in two variables
Linear equation in two variablesLinear equation in two variables
Linear equation in two variablesMRXNOOBGAMING
 
Linear equations Class 10 by aryan kathuria
Linear equations Class 10 by aryan kathuriaLinear equations Class 10 by aryan kathuria
Linear equations Class 10 by aryan kathuriaDhiraj Singh
 
Maths ppt For Linear Equation In One Variable Class 10th!!
Maths ppt For Linear Equation In One Variable Class 10th!!Maths ppt For Linear Equation In One Variable Class 10th!!
Maths ppt For Linear Equation In One Variable Class 10th!!Akshit Kanaujia
 
Linearequationintwovariable 120626053452-phpapp02
Linearequationintwovariable 120626053452-phpapp02Linearequationintwovariable 120626053452-phpapp02
Linearequationintwovariable 120626053452-phpapp02Vineet Mehta
 
prashant tiwari ppt on maths
prashant tiwari ppt on mathsprashant tiwari ppt on maths
prashant tiwari ppt on mathsPrashant tiwari
 
Polynomials And Linear Equation of Two Variables
Polynomials And Linear Equation of Two VariablesPolynomials And Linear Equation of Two Variables
Polynomials And Linear Equation of Two VariablesAnkur Patel
 
Linear equation in tow variable
Linear equation in tow variableLinear equation in tow variable
Linear equation in tow variableRufus Arul
 
Pair of linear equation in two variables
Pair of linear equation in two variables Pair of linear equation in two variables
Pair of linear equation in two variables shivangi gupta
 
Linear equations in Two Variable
Linear equations in Two VariableLinear equations in Two Variable
Linear equations in Two VariableAbhinav Somani
 
Ultimate guide to systems of equations
Ultimate guide to systems of equationsUltimate guide to systems of equations
Ultimate guide to systems of equationskhyps13
 
Lecture 11 systems of nonlinear equations
Lecture 11 systems of nonlinear equationsLecture 11 systems of nonlinear equations
Lecture 11 systems of nonlinear equationsHazel Joy Chong
 
Linear equation in two variable
Linear equation in two variableLinear equation in two variable
Linear equation in two variableNadeem Uddin
 
Pair of linear equations in two variable
Pair of linear equations in two variablePair of linear equations in two variable
Pair of linear equations in two variableBuddhimaan Chanakya
 
Linear equation in 2 variable class 10
Linear equation in 2 variable class 10Linear equation in 2 variable class 10
Linear equation in 2 variable class 10AadhiSXA
 
pairs of linear equation in two variable
pairs of linear equation in two variablepairs of linear equation in two variable
pairs of linear equation in two variableJashan Kainth
 
Linear equation in 2 variables
Linear equation in 2 variablesLinear equation in 2 variables
Linear equation in 2 variablesavb public school
 
Linear equations in two variables
Linear equations in two variablesLinear equations in two variables
Linear equations in two variablesvijayapatil27
 

Similar to Maths ppt linear equations in two variables (20)

Linear equation in two variables
Linear equation in two variablesLinear equation in two variables
Linear equation in two variables
 
Linear equations
Linear equationsLinear equations
Linear equations
 
Linear equations Class 10 by aryan kathuria
Linear equations Class 10 by aryan kathuriaLinear equations Class 10 by aryan kathuria
Linear equations Class 10 by aryan kathuria
 
Maths
MathsMaths
Maths
 
Maths ppt For Linear Equation In One Variable Class 10th!!
Maths ppt For Linear Equation In One Variable Class 10th!!Maths ppt For Linear Equation In One Variable Class 10th!!
Maths ppt For Linear Equation In One Variable Class 10th!!
 
Linearequationintwovariable 120626053452-phpapp02
Linearequationintwovariable 120626053452-phpapp02Linearequationintwovariable 120626053452-phpapp02
Linearequationintwovariable 120626053452-phpapp02
 
prashant tiwari ppt on maths
prashant tiwari ppt on mathsprashant tiwari ppt on maths
prashant tiwari ppt on maths
 
Polynomials And Linear Equation of Two Variables
Polynomials And Linear Equation of Two VariablesPolynomials And Linear Equation of Two Variables
Polynomials And Linear Equation of Two Variables
 
Linear equation in tow variable
Linear equation in tow variableLinear equation in tow variable
Linear equation in tow variable
 
Pair of linear equation in two variables
Pair of linear equation in two variables Pair of linear equation in two variables
Pair of linear equation in two variables
 
Linear equations in Two Variable
Linear equations in Two VariableLinear equations in Two Variable
Linear equations in Two Variable
 
Ultimate guide to systems of equations
Ultimate guide to systems of equationsUltimate guide to systems of equations
Ultimate guide to systems of equations
 
Class 3.pdf
Class 3.pdfClass 3.pdf
Class 3.pdf
 
Lecture 11 systems of nonlinear equations
Lecture 11 systems of nonlinear equationsLecture 11 systems of nonlinear equations
Lecture 11 systems of nonlinear equations
 
Linear equation in two variable
Linear equation in two variableLinear equation in two variable
Linear equation in two variable
 
Pair of linear equations in two variable
Pair of linear equations in two variablePair of linear equations in two variable
Pair of linear equations in two variable
 
Linear equation in 2 variable class 10
Linear equation in 2 variable class 10Linear equation in 2 variable class 10
Linear equation in 2 variable class 10
 
pairs of linear equation in two variable
pairs of linear equation in two variablepairs of linear equation in two variable
pairs of linear equation in two variable
 
Linear equation in 2 variables
Linear equation in 2 variablesLinear equation in 2 variables
Linear equation in 2 variables
 
Linear equations in two variables
Linear equations in two variablesLinear equations in two variables
Linear equations in two variables
 

More from gobilladraksharani

More from gobilladraksharani (10)

MILLETS
MILLETSMILLETS
MILLETS
 
communal harmony
communal harmonycommunal harmony
communal harmony
 
How i taught my grandmother to read
How i taught my grandmother to readHow i taught my grandmother to read
How i taught my grandmother to read
 
The brook
The brookThe brook
The brook
 
Oh i wish i looked after me teeth
Oh i wish i looked after me teethOh i wish i looked after me teeth
Oh i wish i looked after me teeth
 
Topic villaforsale-130612020511-phpapp02
Topic villaforsale-130612020511-phpapp02Topic villaforsale-130612020511-phpapp02
Topic villaforsale-130612020511-phpapp02
 
Circles class 9
Circles class 9Circles class 9
Circles class 9
 
Ppt on the ant and the cricket
Ppt on the ant and the cricketPpt on the ant and the cricket
Ppt on the ant and the cricket
 
Science force and laws of motion
Science  force and laws of motionScience  force and laws of motion
Science force and laws of motion
 
Fibre to fabric
Fibre to fabricFibre to fabric
Fibre to fabric
 

Recently uploaded

Dementia (Alzheimer & vasular dementia).
Dementia (Alzheimer & vasular dementia).Dementia (Alzheimer & vasular dementia).
Dementia (Alzheimer & vasular dementia).Mohamed Rizk Khodair
 
The Benefits and Challenges of Open Educational Resources
The Benefits and Challenges of Open Educational ResourcesThe Benefits and Challenges of Open Educational Resources
The Benefits and Challenges of Open Educational Resourcesaileywriter
 
2024_Student Session 2_ Set Plan Preparation.pptx
2024_Student Session 2_ Set Plan Preparation.pptx2024_Student Session 2_ Set Plan Preparation.pptx
2024_Student Session 2_ Set Plan Preparation.pptxmansk2
 
Danh sách HSG Bộ môn cấp trường - Cấp THPT.pdf
Danh sách HSG Bộ môn cấp trường - Cấp THPT.pdfDanh sách HSG Bộ môn cấp trường - Cấp THPT.pdf
Danh sách HSG Bộ môn cấp trường - Cấp THPT.pdfQucHHunhnh
 
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT VẬT LÝ 2024 - TỪ CÁC TRƯỜNG, TRƯ...
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT VẬT LÝ 2024 - TỪ CÁC TRƯỜNG, TRƯ...TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT VẬT LÝ 2024 - TỪ CÁC TRƯỜNG, TRƯ...
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT VẬT LÝ 2024 - TỪ CÁC TRƯỜNG, TRƯ...Nguyen Thanh Tu Collection
 
An Overview of the Odoo 17 Discuss App.pptx
An Overview of the Odoo 17 Discuss App.pptxAn Overview of the Odoo 17 Discuss App.pptx
An Overview of the Odoo 17 Discuss App.pptxCeline George
 
Features of Video Calls in the Discuss Module in Odoo 17
Features of Video Calls in the Discuss Module in Odoo 17Features of Video Calls in the Discuss Module in Odoo 17
Features of Video Calls in the Discuss Module in Odoo 17Celine George
 
Telling Your Story_ Simple Steps to Build Your Nonprofit's Brand Webinar.pdf
Telling Your Story_ Simple Steps to Build Your Nonprofit's Brand Webinar.pdfTelling Your Story_ Simple Steps to Build Your Nonprofit's Brand Webinar.pdf
Telling Your Story_ Simple Steps to Build Your Nonprofit's Brand Webinar.pdfTechSoup
 
How to the fix Attribute Error in odoo 17
How to the fix Attribute Error in odoo 17How to the fix Attribute Error in odoo 17
How to the fix Attribute Error in odoo 17Celine George
 
UNIT – IV_PCI Complaints: Complaints and evaluation of complaints, Handling o...
UNIT – IV_PCI Complaints: Complaints and evaluation of complaints, Handling o...UNIT – IV_PCI Complaints: Complaints and evaluation of complaints, Handling o...
UNIT – IV_PCI Complaints: Complaints and evaluation of complaints, Handling o...Sayali Powar
 
Basic_QTL_Marker-assisted_Selection_Sourabh.ppt
Basic_QTL_Marker-assisted_Selection_Sourabh.pptBasic_QTL_Marker-assisted_Selection_Sourabh.ppt
Basic_QTL_Marker-assisted_Selection_Sourabh.pptSourabh Kumar
 
Capitol Tech Univ Doctoral Presentation -May 2024
Capitol Tech Univ Doctoral Presentation -May 2024Capitol Tech Univ Doctoral Presentation -May 2024
Capitol Tech Univ Doctoral Presentation -May 2024CapitolTechU
 
50 ĐỀ LUYỆN THI IOE LỚP 9 - NĂM HỌC 2022-2023 (CÓ LINK HÌNH, FILE AUDIO VÀ ĐÁ...
50 ĐỀ LUYỆN THI IOE LỚP 9 - NĂM HỌC 2022-2023 (CÓ LINK HÌNH, FILE AUDIO VÀ ĐÁ...50 ĐỀ LUYỆN THI IOE LỚP 9 - NĂM HỌC 2022-2023 (CÓ LINK HÌNH, FILE AUDIO VÀ ĐÁ...
50 ĐỀ LUYỆN THI IOE LỚP 9 - NĂM HỌC 2022-2023 (CÓ LINK HÌNH, FILE AUDIO VÀ ĐÁ...Nguyen Thanh Tu Collection
 
philosophy and it's principles based on the life
philosophy and it's principles based on the lifephilosophy and it's principles based on the life
philosophy and it's principles based on the lifeNitinDeodare
 
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文中 央社
 
Removal Strategy _ FEFO _ Working with Perishable Products in Odoo 17
Removal Strategy _ FEFO _ Working with Perishable Products in Odoo 17Removal Strategy _ FEFO _ Working with Perishable Products in Odoo 17
Removal Strategy _ FEFO _ Working with Perishable Products in Odoo 17Celine George
 
factors influencing drug absorption-final-2.pptx
factors influencing drug absorption-final-2.pptxfactors influencing drug absorption-final-2.pptx
factors influencing drug absorption-final-2.pptxSanjay Shekar
 
Open Educational Resources Primer PowerPoint
Open Educational Resources Primer PowerPointOpen Educational Resources Primer PowerPoint
Open Educational Resources Primer PowerPointELaRue0
 
[GDSC YCCE] Build with AI Online Presentation
[GDSC YCCE] Build with AI Online Presentation[GDSC YCCE] Build with AI Online Presentation
[GDSC YCCE] Build with AI Online PresentationGDSCYCCE
 

Recently uploaded (20)

Dementia (Alzheimer & vasular dementia).
Dementia (Alzheimer & vasular dementia).Dementia (Alzheimer & vasular dementia).
Dementia (Alzheimer & vasular dementia).
 
The Benefits and Challenges of Open Educational Resources
The Benefits and Challenges of Open Educational ResourcesThe Benefits and Challenges of Open Educational Resources
The Benefits and Challenges of Open Educational Resources
 
Word Stress rules esl .pptx
Word Stress rules esl               .pptxWord Stress rules esl               .pptx
Word Stress rules esl .pptx
 
2024_Student Session 2_ Set Plan Preparation.pptx
2024_Student Session 2_ Set Plan Preparation.pptx2024_Student Session 2_ Set Plan Preparation.pptx
2024_Student Session 2_ Set Plan Preparation.pptx
 
Danh sách HSG Bộ môn cấp trường - Cấp THPT.pdf
Danh sách HSG Bộ môn cấp trường - Cấp THPT.pdfDanh sách HSG Bộ môn cấp trường - Cấp THPT.pdf
Danh sách HSG Bộ môn cấp trường - Cấp THPT.pdf
 
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT VẬT LÝ 2024 - TỪ CÁC TRƯỜNG, TRƯ...
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT VẬT LÝ 2024 - TỪ CÁC TRƯỜNG, TRƯ...TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT VẬT LÝ 2024 - TỪ CÁC TRƯỜNG, TRƯ...
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT VẬT LÝ 2024 - TỪ CÁC TRƯỜNG, TRƯ...
 
An Overview of the Odoo 17 Discuss App.pptx
An Overview of the Odoo 17 Discuss App.pptxAn Overview of the Odoo 17 Discuss App.pptx
An Overview of the Odoo 17 Discuss App.pptx
 
Features of Video Calls in the Discuss Module in Odoo 17
Features of Video Calls in the Discuss Module in Odoo 17Features of Video Calls in the Discuss Module in Odoo 17
Features of Video Calls in the Discuss Module in Odoo 17
 
Telling Your Story_ Simple Steps to Build Your Nonprofit's Brand Webinar.pdf
Telling Your Story_ Simple Steps to Build Your Nonprofit's Brand Webinar.pdfTelling Your Story_ Simple Steps to Build Your Nonprofit's Brand Webinar.pdf
Telling Your Story_ Simple Steps to Build Your Nonprofit's Brand Webinar.pdf
 
How to the fix Attribute Error in odoo 17
How to the fix Attribute Error in odoo 17How to the fix Attribute Error in odoo 17
How to the fix Attribute Error in odoo 17
 
UNIT – IV_PCI Complaints: Complaints and evaluation of complaints, Handling o...
UNIT – IV_PCI Complaints: Complaints and evaluation of complaints, Handling o...UNIT – IV_PCI Complaints: Complaints and evaluation of complaints, Handling o...
UNIT – IV_PCI Complaints: Complaints and evaluation of complaints, Handling o...
 
Basic_QTL_Marker-assisted_Selection_Sourabh.ppt
Basic_QTL_Marker-assisted_Selection_Sourabh.pptBasic_QTL_Marker-assisted_Selection_Sourabh.ppt
Basic_QTL_Marker-assisted_Selection_Sourabh.ppt
 
Capitol Tech Univ Doctoral Presentation -May 2024
Capitol Tech Univ Doctoral Presentation -May 2024Capitol Tech Univ Doctoral Presentation -May 2024
Capitol Tech Univ Doctoral Presentation -May 2024
 
50 ĐỀ LUYỆN THI IOE LỚP 9 - NĂM HỌC 2022-2023 (CÓ LINK HÌNH, FILE AUDIO VÀ ĐÁ...
50 ĐỀ LUYỆN THI IOE LỚP 9 - NĂM HỌC 2022-2023 (CÓ LINK HÌNH, FILE AUDIO VÀ ĐÁ...50 ĐỀ LUYỆN THI IOE LỚP 9 - NĂM HỌC 2022-2023 (CÓ LINK HÌNH, FILE AUDIO VÀ ĐÁ...
50 ĐỀ LUYỆN THI IOE LỚP 9 - NĂM HỌC 2022-2023 (CÓ LINK HÌNH, FILE AUDIO VÀ ĐÁ...
 
philosophy and it's principles based on the life
philosophy and it's principles based on the lifephilosophy and it's principles based on the life
philosophy and it's principles based on the life
 
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
 
Removal Strategy _ FEFO _ Working with Perishable Products in Odoo 17
Removal Strategy _ FEFO _ Working with Perishable Products in Odoo 17Removal Strategy _ FEFO _ Working with Perishable Products in Odoo 17
Removal Strategy _ FEFO _ Working with Perishable Products in Odoo 17
 
factors influencing drug absorption-final-2.pptx
factors influencing drug absorption-final-2.pptxfactors influencing drug absorption-final-2.pptx
factors influencing drug absorption-final-2.pptx
 
Open Educational Resources Primer PowerPoint
Open Educational Resources Primer PowerPointOpen Educational Resources Primer PowerPoint
Open Educational Resources Primer PowerPoint
 
[GDSC YCCE] Build with AI Online Presentation
[GDSC YCCE] Build with AI Online Presentation[GDSC YCCE] Build with AI Online Presentation
[GDSC YCCE] Build with AI Online Presentation
 

Maths ppt linear equations in two variables

  • 1.
  • 2. System of equations A pair of linear equations in two variables is said to form a system of simultaneous linear equations. For Example, 2x – 3y + 4 = 0 x + 7y – 1 = 0 Form a system of two linear equations in variables x and y.
  • 3. The general form of a linear equation in two variables x and y is ax + by + c = 0 , a and b is not equal to zero, where a, b and c being real numbers. A solution of such an equation is a pair of values, One for x and the other for y, Which makes two sides of the equation equal. Every linear equation in two variables has infinitely many solutions which can be represented on a certain line.
  • 4. GRAPHICAL SOLUTIONS OF A LINEAR EQUATION Let us consider the following system of two simultaneous linear equations in two variable. 2x – y = -1 3x + 2y = 9 Here we assign any value to one of the two variables and then determine the value of the other variable from the given equation.
  • 5. For the equation 2x –y = -1 ---(1) 2x +1 = y Y = 2x + 1 3x + 2y = 9 --- (2) 2y = 9 – 3x Y = 9-3x X 0 2 Y 1 5 X 3 -1 Y 0 6
  • 7. Let us take an example x + 2y = -1 ------------------ (i) 2x – 3y = 12 -----------------(ii)
  • 8. SUBSTITUTION METHOD x + 2y = -1 x = -2y -1 ------- (iii) Substituting the value of x in equation (ii), we get 2x – 3y = 12 2 ( -2y – 1) – 3y = 12 - 4y – 2 – 3y = 12 - 7y = 14 , y = -2 ,
  • 9. SUBSTITUTION Putting the value of y in eq. (iii), we get x = - 2y -1 x = - 2 x (-2) – 1 = 4 – 1 = 3 Hence the solution of the equation is ( 3, - 2 )
  • 10. ELIMINATION METHOD • In this method, we eliminate one of the two variables to obtain an equation in one variable which can easily be solved. Putting the value of this variable in any of the given equations, The value of the other variable can be obtained. • For example: we want to solve, 3x + 2y = 11 2x + 3y = 4
  • 11. Let 3x + 2y = 11 --------- (i) 2x + 3y = 4 ---------(ii) Multiply 3 in equation (i) and 2 in equation (ii) and subtracting eq. iv from iii, we get 9x + 6y = 33 ------ (iii) 4x + 6y = 8 ------- (iv) 5x = 25 x = 5
  • 12. • putting the value of y in equation (ii) we get, 2x + 3y = 4 2 x 5 + 3y = 4 10 + 3y = 4 3y = 4 – 10 3y = - 6 y = - 2 Hence, x = 5 and y = -2