NCERT Solutions for Class 9 Maths Chapter 4 : Linear Equations In Two Variables

Content Curator

The NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations In Two Variables are provided in this article. Linear equations in two variables is represented as ax + by + c = 0. When a linear equation has two variables, it is known as a linear equation in two variables.

Class 9 Maths Chapter 4 Linear Equations In Two Variables belong to Unit 2 Algebra which has a weightage of 20 marks in the Class 9 Maths Examination. NCERT Solutions for Class 9 Maths for Chapter 4 cover the following important concepts:

Download: NCERT Solutions for Class 9 Mathematics Chapter 4 pdf

NCERT Solutions for Class 9 Maths Chapter 4

The Chapter 4 Class 9 Maths are given below:

NCERT Solutions

Important Topics in Class 9 Maths Chapter 4 Linear Equations in Two Variables

Important Topics in Class 9 Maths Chapter 4 Linear Equations in Two Variables are elaborated below:

Introduction to Two-variable Linear Equations of the Type ax + by + c = 0

Example: Show an equation in the form of ax + by + c = 0 (Where a, b, and c are real numbers and constants.)

Solution: An equation in the form of ax + by + c = 0 can be demonstrated as:
x + 2y = 6; 2x + y = 7.

Using Bar Graph to Plot Linear Equation and Justifying any Point on a Line

The graph of a linear equation in two variables is considered as a line. If an equation is linear, we can graph it by finding any two solutions, (x1,y1)(x1,y1) and (x2,y2)(x2,y2). After plotting these two points, we can draw the line connecting them.

Example: Given a linear function, how do can you graph plotting points?

Solution: We can graph the plotting points:

First, slecet a minimum of two input values.
Further, calculate the required function at each input value.
Then use the resulting output values to recognize the coordinate pairs involved.
Plot the coordinate pairs on a grid.
Now connect the lines through the points.

Ratio and Proportion

A ratio, in linear equations, is a comparison of two given quantities. A proportion, however, is an equality of two given ratios.

Example: Consider that ⅘ is a ratio and the proportion it has is 20/25 = ⅘. Solve and evaluate its proportional statement.

Solution: To solve its proportional statement, we have to:
20/25 = ⅘
20 x 5 = 25 x 4
100 = 100

NCERT Solutions for Class 9 Maths Chapter 4 Exercises:

The detailed solutions for all the NCERT Solutions for Linear Equations in Two Variables under different exercises are:

Also Read:

Important Chapter Related Links
Linear Equations in Two Variables MCQs	Consistent Systems of Linear Equations	Pair of Linear Equations In Two Variables Important Questions
Substitution Method of Solving a Pair of Linear Equations	Graph of a Linear Equation in Two Variables	Linear equations: Standard Forms

Also Read:

Math Study Guides
Maths Important Formulas	Maths MCQs	Comparison Articles in Maths
Difference Between Topics in Maths	Math Study Material	Algebra
Trigonometry	Number Systems	Mensuration
Math Formula	NCERT Solutions for Class 9 Maths	Geometry

CBSE X Related Questions

1.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$
View Solution
2.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- Assertion (A) is true, but Reason (R) is false.
- Assertion (A) is false, but Reason (R) is true.
View Solution
3.
If the zeroes of a polynomial p(x) are $-3$ and 8, then p(x) equals
- $x^2 + 5x - 4$
- $(x + 3) (-x + 8)$
- $a(x^2 + 5x - 24)$
- $x^2 - 24$
View Solution
4.
Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is
- $\frac{5}{12}$
- $\frac{5}{6}$
- $1$
- $0$
View Solution
5.
PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If OP = 13 cm, then find the length AB and PA.
View Solution
6.
Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
View Solution

View All

Similar Mathematics Concepts

Linear Equation in Two Variables: Solutions & Examples

Consistent and Inconsistent System of Equations

Linear Equations in Two Variables MCQs

Important Questions for Class 12 Maths Linear Equations in Two Variables

NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.1 Solutions

NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.2 Solutions

NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.3 Solutions

NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.4 Solutions

Linear Equations Formula: Derivation & Examples

Mathematics Preparation Guides

Statistics: Mean, Median, Variance and Cumulative Frequency Curve

Remainder Theorem: Definition, Steps & Examples

Angle Formula: Definition, Different Types, Solved Example

Trapezoids: Isosceles, Scalene Properties, Area, Properties, Examples

Quadrilateral Angle Sum Property: Theorem, Types & Example

Frequency Polygons: Steps, Formula & Examples

Area of Parallelogram: How to Calculate Area of Parallelogram?

Congruence of Triangles: SSS, SAS, ASA & RHS Rules

Quadrilateral Formulas: Types and Properties

Properties of Triangle: Types, Formulas & Examples

Class 9 Maths MCQ: Chapter-wise with Solutions

Properties of Parallel Lines: Transitive & Symmetric Properties

Isosceles triangle: Types, Properties, Angles & Examples

Operations on Rational Numbers:Rules, Properties & Examples

Addition and Subtraction of Integers: Rules & Examples

Scalene Triangle: Types, Formulas, Properties & Examples

Quadrant: Types, Sign Convention & Examples

Rationalize the Denominator: Explanation and Solved Examples

Area of a Kite: Formula, Derivation & Examples

Volume of a Pyramid: Formula and Solved Example

Mathematics NCERT Solutions

Linear Equation in Two Variables: Graph, Elimination and Substitution

Types of Triangles: Important Terms, Scalene, Acute, and Obtuse Triangle

Formula Of Perimeter Shapes

Sphere Formula: Diameter, Surface Area and Volume

Ordinate: Abscissa, Plotting Ordinates, Relation, Solved Examples

Integers as Exponents: Explanation, Rules and Method of Solving

Central Tendency: Definition, Methods and Sample Questions

Line Segment: Definition, Measurement and Examples

Line, Line Segment and Ray: Differentiation and Sample Questions

Area of Equilateral Triangle, Perimeter & Altitude Formulas

You can also check

NCERT Solutions for Class 9 Maths Chapter 4 : Linear Equations In Two Variables

NCERT Solutions for Class 9 Maths Chapter 4

Important Topics in Class 9 Maths Chapter 4 Linear Equations in Two Variables

Introduction to Two-variable Linear Equations of the Type ax + by + c = 0

Using Bar Graph to Plot Linear Equation and Justifying any Point on a Line

Ratio and Proportion

NCERT Solutions for Class 9 Maths Chapter 4 Exercises:

CBSE X Related Questions

1.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

2.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

3.
If the zeroes of a polynomial p(x) are $-3$ and 8, then p(x) equals

4.
Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is

5.
PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If OP = 13 cm, then find the length AB and PA.

6.
Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

NCERT Solutions for Class 9 Maths Chapter 4 : Linear Equations In Two Variables

NCERT Solutions for Class 9 Maths Chapter 4

Important Topics in Class 9 Maths Chapter 4 Linear Equations in Two Variables

Introduction to Two-variable Linear Equations of the Type ax + by + c = 0

Using Bar Graph to Plot Linear Equation and Justifying any Point on a Line

Ratio and Proportion

NCERT Solutions for Class 9 Maths Chapter 4 Exercises:

CBSE X Related Questions

1.Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

2.Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent. Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

3.If the zeroes of a polynomial p(x) are $-3$ and 8, then p(x) equals

4.Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is

5.PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If OP = 13 cm, then find the length AB and PA.

6.Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

2.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

3.
If the zeroes of a polynomial p(x) are $-3$ and 8, then p(x) equals

4.
Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is

5.
PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If OP = 13 cm, then find the length AB and PA.

6.
Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.