In the world of algebra, a pair of linear equations is a conversation between two lines seeking a common ground. Have you ever tried to figure out the number of certain items you can buy within a particular budget? You can do this using linear equations!!! Linear Equations in Two Variables define the relationship between two specific quantities. It includes speed and distance, cost and profit, purchase and sales, and so on. These NCERT Solutions for Class 9 Maths help to simplify the process of finding solutions using substitution and plotting, and give step-by-step solutions to all the exercise problems in the Class 9 Maths Book.
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Solving a pair of linear equations is like finding the intersection where two different paths agree. It is one of the most important chapters in class 9 as well as for higher classes. These NCERT Solutions for Class 9 are trustworthy and reliable, as they are created by subject matter experts at Careers360, making them an essential resource for exam preparation. Many toppers rely on NCERT Solutions since they are designed as per the latest syllabus. For additional practice, students can also refer to the NCERT exemplar solutions and notes. For full syllabus coverage and solved exercises as well as a downloadable PDF, please visit this NCERT article.
To make maths learning easier, Careers360 experts have created these
NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables. Students can also access these solutions in PDF form.
NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Exercise 4.1 Page Number: 57 Number of Questions: 2 |
Answer:
Let the cost of a notebook be Rs x and that of a pen be Rs y.
According to the given condition: The cost of a notebook is twice the cost of a pen.
Thus, $x=2y$
$\Rightarrow x-2y=0$
Question 2: (i) Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of a, b and c in each case: $2x + 3y = 9.3\bar{5}$
Answer:
Given : $2x + 3y = 9.3\bar{5}$
$\Rightarrow 2x + 3y - 9.3\bar{5}=0$
Here , $a=2, b=3$ and $c = - 9.3\bar{5}$
Question 2: (ii) Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of a, b and c in each case: $x - \frac{y}{5} - 10 = 0$
Answer:
Given:
$x - \frac{y}{5} - 10 = 0$
$\Rightarrow x - \frac{y}{5} - 10 = 0$
Here,
$a=1$,
$b=\frac{-1}{5}$
$c = -10$
Question 2: (iii) Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of a, b and c in each case: $-2x + 3y = 6$
Answer:
Given :
$-2x + 3y = 6$
$\Rightarrow -2x + 3y - 6=0$
Here , $a= -2, b=3$ and $c = -6$
Question 2: (iv) Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of a, b and c in each case: $x =3y$
Answer:
Given : $x =3y$
$\Rightarrow x -3y=0$
Here , $a= 1, b= -3$ and $c =0$
Question 2: (v) Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of a, b and c in each case: $2x = - 5y$
Answer:
Given : $2x = - 5y$
$\Rightarrow 2x + 5y=0$
Here , $a=2, b= 5$ and $c =0$
Question 2: (vi) Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of a, b and c in each case: $3x + 2 = 0$
Answer:
Given : $3x + 2 = 0$
$\Rightarrow 3x + 2 = 0$
Here , $a= 3, b=0$ and $c =2$
Question 2: (vii) Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of a, b and c in each case: $y -2 = 0$
Answer:
Given : $y -2 = 0$
$\Rightarrow 0.x+y -2 = 0$
Here, $a=0, b= 1$ and $c = -2$
Question 2: (viii) Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of a, b and c in each case: $5 = 2x$
Answer:
Given: $5 = 2x$
$\Rightarrow 2x+0.y-5=0$
Here, $a=2, b= 0$ and $c = -5$
NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Exercise 4.2 Page Number: 59 Number of Questions: 4 |
Question 1: Which one of the following options is true, and why? $y = 3x + 5$ has
(i) a unique solution,
(ii) only two solutions,
(iii) infinitely many solutions
Answer:
Given : $y = 3x + 5$
This equation is of a line and a line has infinite points on it and each point is a solution Thus, (iii) infinitely many solutions is the correct option.
Question 2: Write four solutions for each of the following equations:
(i) $2x + y = 7$ (ii) $\pi x +y = 9$ (iii) $x = 4y$
Answer:
(i) Given : $2x + y = 7$
Putting x=0, we have , $y=7-2\times 0=7$ means $(0,7)$ is a solution.
Putting x=1, we have , $y=7-2\times 1=5$ means $(1,5)$ is a solution.
Putting x=2, we have , $y=7-2\times 2=3$ means $(2,3)$ is a solution.
Putting x=3, we have , $y=7-2\times 3=1$ means $(3,1)$ is a solution.
The four solutions are : $(0,7),(1,5),(2,3),(3,1)$ .
(ii) Given : $\pi x +y = 9$
Putting x=0, we have , $y=9-\pi \times 0=9$ means $(0,9)$ is a solution.
Putting x=1, we have , $y=9-\pi \times 1=9-\pi$ means $(1,9-\pi )$ is a solution.
Putting x=2, we have , $y=9-\pi \times 2=9-2\pi$ means $(2,9-2\pi )$ is a solution.
Putting x=3, we have , $y=9-\pi \times 3=9-3\pi$ means $(3,9-3\pi )$ is a solution.
The four solutions are : $(0,9),(1,9-\pi ),(2,9-2\pi ),(3,9-3\pi )$ .
(iii) Given: $x = 4y$
Putting x=0, we have , $y=\frac{0}{4}=0$ means $(0,0)$ is a solution.
Putting x=1, we have , $y=\frac{1}{4}$ means $(1,\frac{1}{4})$ is a solution.
Putting x=2, we have , $y=\frac{2}{4}=\frac{1}{2}$ means $(2,\frac{1}{2})$ is a solution.
Putting x=3, we have , $y=\frac{3}{4}$ means $(3,\frac{3}{4})$ is a solution.
The four solutions are : $(0,0)$ , $(1,\frac{1}{4})$ , $(2,\frac{1}{2})$ and $(3,\frac{3}{4})$ .
Question 3: (i) Check which of the following are solutions of the equation $x - 2y = 4$ and which are not: ((0,2)
Answer:
(i) Given : $x - 2y = 4$
Putting $(0,2)$ ,
we have , $x - 2y = 0-2(2)=-4\neq 4$
Therefore, $(0,2)$ is not a solution of $x - 2y = 4$ .
Question 3: (ii) Check which of the following are solutions of the equation $x - 2y = 4$ and which are not: (2,0)
Answer:
Given : $x - 2y = 4$
Putting (2,0),
we have , $x - 2y = 2-2(0)=2\neq 4$
Therefore, (2,0) is not a solution of $x - 2y = 4$.
Question 3: (iii) Check which of the following are solutions of the equation $x - 2y = 4$ and which are not: (4,0)
Answer:
Given : $x - 2y = 4$
Putting (4,0),
we have , $x - 2y = 4-2(0)=4=4$
Therefore, (4,0) is a solution of $x - 2y = 4$.
Question 3: (iv) Check which of the following are solutions of the equation $x - 2y = 4$ and which are not: $(\sqrt2, 4\sqrt2)$
Answer:
Given : $x - 2y = 4$
Putting $(\sqrt2 , 4\sqrt2)$ ,
we have , $x - 2y =\sqrt{2}-2(4\sqrt{2})=\sqrt{2}-8\sqrt{2}=-7\sqrt{2}\neq 4$
Therefore, $(\sqrt2 , 4\sqrt2)$ is not a solution of $x - 2y = 4$ .
Question 3: (v) Check which of the following are solutions of the equation $x - 2y = 4$ and which are not: (1,1)
Answer:
Given : $x - 2y = 4$
Putting (1,1),
we have , $x - 2y = 1-2(1)=-1\neq 4$
Therefore, (1,1) is not a solution of $x - 2y = 4$ .
Question 4: Find the value of k , if $x = 2$ , $y = 1$ is a solution of the equation $2x + 3y = k$ .
Answer:
Given : $2x + 3y = k$
Putting (2,1),
we have , $k=2x + 3y = 2(2)+3(1)=4+3=7$
Therefore, k=7 for $2x + 3y = k$ putting x=2 and y=1.
Exercise-wise NCERT Solutions of Linear Equations in Two Variables Class 9 Maths Chapter 4 are provided in the link below.
Question: Find the value of $y$ in the equation $ 2x + 3y = 12 $ when $x = 3 $.
Answer:
First, substitute $x = 3 $ into the equation:
We get, $2(3) + 3y = 12 \Rightarrow 6 + 3y = 12$
$3y = 12 - 6 = 6 \Rightarrow y = \frac{6}{3} = 2$
Thus, the value of $y$ is 2.
The topics discussed in the NCERT Linear Equations in Two Variables Class 9 solutions are:
The equations with two variables are called Linear Equations. The general form of a linear equation in two variables is ax+by=c, where a,b,c are real numbers and $a \neq 0$ and $b \neq 0 $.
The linear equations in two variables have infinitely many solutions. Every solution of linear equations in two variables is a point on the equation's graph.
These approaches will help students deal with Class 9 Maths Chapter 4 Question Answers efficiently.
1. Understand the standard form: A linear equation consisting of two variables uses the form of $ax+by+c=0$ for all its components to be real numbers and also $a, b \neq 0$.
2. Know that each solution is a pair of values: The equation accepts ordered pairs (x,y) which solve the equation during substitution.
3. Use substitution to find solutions: Executing different x (or y) value substitutions helps determine corresponding values of the opposite variable.
4. Create tables of values: Make value tables that contain 3–5 solutions to reveal the relationship between the x and y variables.
5. Graph the solutions: Draw the pairs of solution points on a Cartesian coordinate system to see that they form a straight line.
6. Interpret the meaning of infinite solutions: The system of a linear equation that includes two variables can have numerous solutions defined through points which exist on the same straight line.
We at Careers360 compiled all the NCERT class 9 Maths solutions in one place for easy student reference. The following links will allow you to access them.
Also, read,
We at Careers360 provide the links for Class 9 NCERT Books and NCERT Syllabus, making it easily accessible to the students. Below are the links for other study resources of NCERT Class 9.
Frequently Asked Questions (FAQs)
Yes, practising all the questions and formulas related to Maths Class 9 Chapter 4 is essential to perform well in board exams. Trusted educational websites, such as the Careers360 website, provide accurate and easy-to-understand solutions, which can be beneficial for students to score higher marks. Apart from exam preparation, these solutions can also assist in solving homework and assignments.
There are 2 exercises in this chapter consisting of 2 and 4 questions, respectively, covering questions from the basics to the advanced level of problem-solving.
The key topics include:
NCERT solutions are provided in a very detailed manner, which will give the conceptual clarity to the students. Also, students can take help from these solutions if they are not able to solve it on their own.
Free NCERT Class 9 Maths Chapter 4 solutions are available on many online educational platforms, such as Careers360 and can be accessed in both web and PDF formats for easy practice.
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