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Access and download free PDF worksheets for CBSE Class 9 Mathematics Chapter 4 Linear Equations in Two Variables. These worksheets, designed by experienced teachers, align with the latest syllabus and exam patterns issued by CBSE and NCERT. Engage in daily practice of these Mathematics Class 9 assignments to improve your performance in tests and exams.
Linear Equations in Two Variables Class 9 Maths Class 4 Worksheets
In Class 9, learning about linear equations in two variables is important for understanding algebra. Class 9 Chapter 4 focuses on this topic, teaching students how to work with equations involving two variables. To help students practice and improve their skills, worksheets specifically designed for linear equations in two variables in Class 9 have been created.
These worksheets are like practice exercises that make learning easier. They give students a chance to solve different types of problems related to linear equations in two variables. By using these worksheets, students can become more confident in solving such equations and get better at algebra.
These worksheets are meant to help students understand and apply the concepts taught in Chapter 4 of their Maths class. They are a useful tool for practicing and testing what students have learned about linear equations in two variables. By working through these worksheets, students can strengthen their problem-solving abilities and be better prepared for tests and exams.
Refer to the following worksheet in PDF format for CBSE Class 9 Mathematics. This comprehensive test paper, featuring questions and solutions, will be highly beneficial for your preparation and help you achieve better scores.
Linear Equations in Two Variables Class 9 Maths Class 4 Worksheets PDF
Linear Equations in Two Variables Class 9 Maths with Questions with Answers
Question: What is the general form of a linear equation in two variables?
Answer: The general form of a linear equation in two variables is ax + by + c = 0, where a, b, and c are constants and x and y are variables.
Question: What is the difference between a linear equation and a non-linear equation?
Answer: A linear equation is an equation in which the highest power of the variable(s) is 1, whereas a non-linear equation is an equation in which the highest power of the variable(s) is greater than 1.
Question: How do you solve a linear equation in two variables?
Answer: To solve a linear equation in two variables, you can use substitution or elimination methods. The goal is to isolate one variable, then substitute that expression into the other equation to solve for the other variable.
Question: What is the concept of a solution to a linear equation in two variables?
Answer: A solution to a linear equation in two variables is an ordered pair of values that makes the equation true. For example, if the equation is 2x + 3y = 6, then the solution is (1, 1) because 2(1) + 3(1) = 6.
Question: How do you identify the slope of a line given two points on the line?
Answer: To identify the slope of a line given two points on the line, you can use the formula m = (y2 – y1) / (x2 – x1), where (x1, y1) and (x2, y2) are the two points.
Question: What is the concept of a linear equation in two variables with no solution?
Answer: A linear equation in two variables with no solution is an equation that has no ordered pair of values that makes the equation true. This occurs when the lines formed by the equations are parallel and do not intersect.
Question: How do you identify the equation of a line given two points on the line?
Answer: To identify the equation of a line given two points on the line, you can use the point-slope form of a line, which is y – y1 = m(x – x1), where (x1, y1) is one of the points and m is the slope.
Question: What is the concept of a linear equation in two variables with infinitely many solutions?
Answer: A linear equation in two variables with infinitely many solutions is an equation that has all ordered pairs of values that make the equation true. This occurs when the lines formed by the equations are identical.
Question: How do you identify the equation of a line given the slope and a point on the line?
Answer: To identify the equation of a line given the slope and a point on the line, you can use the point-slope form of a line, which is y – y1 = m(x – x1), where (x1, y1) is the point and m is the slope.
Question: What is the concept of a linear equation in two variables with one solution?
Answer: A linear equation in two variables with one solution is an equation that has exactly one ordered pair of values that makes the equation true. This occurs when the lines formed by the equations intersect at a single point.
Question: Find the value of k for which the pair of linear equations 3x + 2y = 7 and kx + 4y = 14 has no solution.
Answer: To find the value of k, we need to check if the equations are inconsistent. This happens when the equations are parallel, i.e., they have the same slope but different y-intercepts.
Let’s find the slopes of the two equations:
Slope of 3x + 2y = 7: m₁ = -3/2
Slope of kx + 4y = 14: m₂ = -k/4For the equations to be parallel, the slopes must be equal:
-3/2 = -k/4
3k = 8
k = 8/3
Question: Find the value of k for which the pair of linear equations 2x + 3y = 7 and 4x + ky = 14 has a unique solution.
Answer: To find the value of k, we need to check if the equations have a unique solution. This happens when the equations intersect at a single point, i.e., they are not parallel and not coincident.
Let’s find the slopes of the two equations:
Slope of 2x + 3y = 7: m₁ = -2/3
Slope of 4x + ky = 14: m₂ = -4/kFor the equations to intersect at a single point, the slopes must be different:
-2/3 ≠ -4/k
2k ≠ 12
k ≠ 6Therefore, the value of k for which the pair of linear equations has a unique solution is any value other than 6.
Question: Find the value of k for which the pair of linear equations 2x + 3y = 7 and 4x + ky = 14 has infinitely many solutions.
Answer: To find the value of k, we need to check if the equations have infinitely many solutions. This happens when the equations are coincident, i.e., they have the same slope and the same y-intercept.
Let’s find the slopes of the two equations:
Slope of 2x + 3y = 7: m₁ = -2/3
Slope of 4x + ky = 14: m₂ = -4/kFor the equations to be coincident, the slopes must be equal and the y-intercepts must be the same:
-2/3 = -4/k
2k = 12
k = 6Therefore, the value of k for which the pair of linear equations has infinitely many solutions is 6.
Question: Solve the system of linear equations: 2x + 3y = 7 and 4x + 6y = 14.
Answer: To solve the system of linear equations, we can use the substitution method or the elimination method.
Using the substitution method:
From the first equation, express y in terms of x:
2x + 3y = 7
3y = -2x + 7
y = (-2x + 7)/3Substitute y in the second equation:
4x + 6((-2x + 7)/3) = 14
4x – 4x + 42 = 42
42 = 42Therefore, the solution is x = 0 and y = 7/3.
Question: Solve the system of linear equations: 3x + 2y = 13 and 2x + 5y = 17.
Answer: To solve the system of linear equations, we can use the substitution method or the elimination method.
Using the elimination method:
Multiply the first equation by 5 and the second equation by 2:
15x + 10y = 65
4x + 10y = 34Subtract the second equation from the first equation:
11x = 31
x = 31/11Substitute x in the first equation to find y:
3(31/11) + 2y = 13
93/11 + 2y = 13
2y = 13 – 93/11
2y = 143/11 – 93/11
2y = 50/11
y = 25/11Therefore, the solution is x = 31/11 and y = 25/11.
Question: Solve the system of linear equations: 2x – y = 1 and 3x + 2y = 7.
Answer: To solve the system of linear equations, we can use the substitution method or the elimination method.
Using the elimination method:
Multiply the first equation by 2 and the second equation by 1:
4x – 2y = 2
3x + 2y = 7Add the two equations:
7x = 9
x = 9/7Substitute x in the first equation to find y:
2(9/7) – y = 1
18/7 – y = 1
-7y = 1 – 18/7
-7y = 7 – 18
-7y = -11
y = 11/7Therefore, the solution is x = 9/7 and y = 11/7.
Question: Solve the system of linear equations: 3x + 2y = 12 and 2x – y = 1.
Answer: To solve the system of linear equations, we can use the substitution method or the elimination method.
Using the substitution method:
From the second equation, express y in terms of x:
2x – y = 1
y = 2x – 1Substitute y in the first equation:
3x + 2(2x – 1) = 12
3x + 4x – 2 = 12
7x = 14
x = 2Substitute x in the second equation to find y:
2(2) – y = 1
4 – y = 1
-y = -3
y = 3Therefore, the solution is x = 2 and y = 3.
Question: Solve the system of linear equations: 4x + 3y = 11 and 2x – y = 1.
Answer: To solve the system of linear equations, we can use the substitution method or the elimination method.
Using the elimination method:
Multiply the first equation by 1 and the second equation by 3:
4x + 3y = 11
6x – 3y = 3Subtract the second equation from the first equation:
-2x = 8
x = -4Substitute x in the second equation to find y:
2(-4) – y = 1
-8 – y = 1
-y = 9
y = -9Therefore, the solution is x = -4 and y = -9.
Question: Solve the system of linear equations: 3x + 2y = 8 and 2x – y = 1.
Answer: To solve the system of linear equations, we can use the substitution method or the elimination method.
Using the elimination method:
Multiply the first equation by 1 and the second equation by 2:
3x + 2y = 8
4x – 2y = 2Add the two equations:
7x = 10
x = 10/7Substitute x in the second equation to find y:
2(10/7) – y = 1
20/7 – y = 1
-7y = 1 – 20/7
-7y = 7 – 20
-7y = -13
y = 13/7Therefore, the solution is x = 10/7 and y = 13/7.
Question: Solve the system of linear equations: 2x + 3y = 13 and 4x – y = 5.
Answer: To solve the system of linear equations, we can use the substitution method or the elimination method.
Using the elimination method:
Multiply the first equation by 1 and the second equation by 3:
2x + 3y = 13
12x – 3y = 15Subtract the second equation from the first equation:
-10x = -2
x = 2/5Substitute x in the first equation to find y:
2(2/5) + 3y = 13
4/5 + 3y = 13
3y = 13 – 4/5
3y = 65/5 – 4/5
3y = 61/5
y = 61/15Therefore, the solution is x = 2/5 and y = 61/15.
Worksheet Aligned with the Latest Syllabus
The practice worksheet on linear equations in two variables for class 9 has been meticulously crafted to match the current syllabus for CBSE Class 9 Mathematics. Students can easily download the PDF format and practice the questions and answers on a daily basis to strengthen their concepts and problem-solving skills.
Developed by Expert Teachers
The Mathematics Class 9 worksheet has been developed by referring to the most important and frequently asked topics, ensuring that students learn and practice the essential concepts to excel in their examinations. Infinity Learn is the best portal for Printable Worksheets for Class 9 Mathematics students, providing free access to the latest study materials.
Comprehensive Coverage of NCERT Textbook
The practice worksheet on linear equations in two variables for class 9 s has been designed by referring to the NCERT book for Class 9 Mathematics. Regular practice of these printable worksheets will help students secure better scores in Class 9 exams by developing a stronger understanding of the concepts.
Importance of Daily Practice
Daily practice of Mathematics printable worksheets and study materials will help students develop a stronger grasp of all concepts and become proficient in scoring topics. You can easily download and save all revision worksheets for Class 9 Mathematics from Infinity Learn in PDF format without any cost.
Answers and Solutions Provided
The practice sheets have been developed as per the latest course books, and the answers have been provided by our expert teachers. After solving the questions, students can compare their answers with the solutions to identify areas for improvement.
MCQ Questions for Comprehensive Practice
The worksheet includes a variety of MCQ questions covering all topics given in each chapter to help students practice and assess their understanding of the concepts.
Printable Worksheets for Effective Learning
Regular practice of printable worksheets plays a crucial role in gaining a comprehensive understanding of Chapter 4 Linear Equations in Two Variables concepts. Students can download, save, or print all the worksheets, assignments, and practice linear equations in two variables class 9 worksheet with answers in PDF format from Infinity Learn.
Revision and Practice for Upcoming Tests
If you have tests coming up, revise all concepts related to Chapter 4 Linear Equations in Two Variables and then attempt the practice sheet. Infinity Learn also provides a wide range of worksheets for Class 9 Mathematics to further enhance your skills and understanding of the subject.
Linear Equations in Two Variables Class 9 Maths Worksheet FAQs
What is the significance of linear equations in two variables worksheets for students?
Linear equations in two variables worksheets help students understand the concept of equations with two variables and enhance their problem-solving skills.
How many questions are typically found in NCERT Class 9 Maths Chapter 4 on Linear Equations in Two Variables?
NCERT Class 9 Maths Chapter 4 usually contains 16 questions divided into different categories to aid students in understanding linear equations thoroughly.
Why is it essential for students to build a strong foundation in Chapter 4 of Class 9 Maths?
Building a strong foundation in Chapter 4 of Class 9 Maths is crucial as many algebraic concepts in higher grades rely on understanding linear equations in two variables. Additionally, real-life applications like profit calculations require a solid grasp of this topic.
How can linear equations be represented graphically and what do the solutions on the graph signify?
Linear equations can be graphically represented as straight lines, where each point on the line represents a solution to the equation. This visual representation helps in understanding the relationship between variables.
What are the key topics covered in Chapter 4 of CBSE Class 9 Mathematics syllabus related to linear equations in two variables?
The key topics covered in Chapter 4 include the graphical representation of linear equations, solutions of linear equations on a graph, lines passing through the origin, and lines parallel to coordinate axes, providing a comprehensive understanding of this mathematical concept.
