RD Sharma Solutions Class 9 Maths Chapter 13 – Free PDF Download
RD Sharma Solutions for Class 9 Maths Chapter 13 focus on Linear Equations in Two Variables. This chapter introduces the concept of linear equations, which are equations that can be written in the form ax + by + c = 0, where a, b, and c are real numbers, and a and b (the coefficients of x and y) are not equal to zero. Understanding how to solve these equations is key to mastering this topic.
To become proficient in solving linear equations, students should practice the problems provided in the RD Sharma Solutions repeatedly. This will help them improve their skills and solve problems more quickly and accurately.
Students aiming for high marks in exams can benefit from Infinity Learn (IL) by Sri Chaitanya, which offers expertly solved solutions aligned with the CBSE syllabus 2025-26. Chapter 13 covers various methods for finding solutions to linear equations in two variables, as well as how to represent real-life situations using equations.
For example, in a cricket tournament, if the sum of the runs scored by two players, P and Q, is 132, the equation would be represented as follows:
Example: In a cricket tournament, the sum of the runs scored by two players, P and Q, is 132. Represent this in equation form.
Solution: Let a and b represent the total runs scored by players P and Q, respectively. The total sum of runs is 132, so the equation is:
a + b = 132
This is the required equation.
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RD Sharma Solution for Class 9 Chapter 12 - Download PDF
RD Sharma Solutions Class 9 Maths Chapter 13 – Linear Equations in Two Variables Solutions, designed to help students prepare effectively for their exams. By referring to these solutions and practicing the problems, students can boost their confidence and improve their scores.
1. What is a linear equation in two variables?
Answer: A linear equation in two variables is an equation that involves two variables and the highest power of each variable is one. It is in the form of Ax + By = C, where A, B, and C are constants, and x and y are the variables.
2. Give an example of a linear equation in two variables.
Answer: An example of a linear equation in two variables is 2x + 3y = 6.
3. What are the variables in a linear equation?
Answer: In a linear equation, the variables are the unknown values represented by letters, usually x and y, which we need to find.
4. 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, where A and B are not both zero, and A, B, and C are constants.
5. How do you graph a linear equation in two variables?
Answer: To graph a linear equation, find at least two points that satisfy the equation. Plot those points on the graph and draw a straight line through them. This line represents the solution to the equation.
6. What is the solution to a linear equation in two variables?
Answer: The solution to a linear equation in two variables is any ordered pair of numbers (x, y) that makes the equation true.
7. How many solutions does a linear equation in two variables have?
Answer: A linear equation in two variables has infinitely many solutions because there are many pairs of values for x and y that can satisfy the equation.
8. What is a system of linear equations?
Answer: A system of linear equations consists of two or more linear equations involving the same variables. The goal is to find the values of the variables that satisfy all the equations in the system.
9. How do you solve a system of linear equations graphically?
Answer: To solve a system of linear equations graphically, plot both equations on the same graph. The point where the two lines intersect is the solution to the system.
10. What is the substitution method in solving linear equations?
Answer: The substitution method involves solving one equation for one variable and then substituting that expression into the other equation to find the values of the variables.
11. What is the elimination method in solving linear equations?
Answer: The elimination method involves adding or subtracting the equations to eliminate one of the variables, making it easier to solve for the other variable.
12. Can a system of linear equations have no solution?
Answer: Yes, a system of linear equations can have no solution if the lines representing the equations are parallel and do not intersect.
13. What does it mean if the lines representing the equations are parallel?
Answer: If the lines are parallel, it means they never intersect, and hence, the system has no solution.
14. Can a system of linear equations have infinitely many solutions?
Answer: Yes, a system of linear equations can have infinitely many solutions if the equations represent the same line, meaning they are dependent.
15. What is the graphical interpretation of a linear equation in two variables?
Answer: The graphical interpretation of a linear equation is a straight line on a coordinate plane, where every point on the line is a solution to the equation.
16. How do you find the x-intercept of a linear equation?
Answer: To find the x-intercept, set y equal to zero in the equation and solve for x. The x-intercept is the point where the line crosses the x-axis.
17. How do you find the y-intercept of a linear equation?
Answer: To find the y-intercept, set x equal to zero in the equation and solve for y. The y-intercept is the point where the line crosses the y-axis.
18. What does it mean when the slope of a line is zero?
Answer: When the slope of a line is zero, it means the line is horizontal, and there is no change in the y-coordinate as the x-coordinate changes.
19. What does it mean when the slope of a line is undefined?
Answer: When the slope of a line is undefined, it means the line is vertical, and there is no change in the x-coordinate as the y-coordinate changes.
20. What is the slope of the line 3x + 4y = 12?
Answer: To find the slope, rewrite the equation in slope-intercept form (y = mx + b), where m is the slope. The slope of the line 3x + 4y = 12 is -3/4.
21. What is the slope-intercept form of a linear equation?
Answer: The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept.
22. What is the point-slope form of a linear equation?
Answer: The point-slope form of a linear equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
23. How do you convert a linear equation from standard form to slope-intercept form?
Answer: To convert from standard form Ax + By = C to slope-intercept form y = mx + b, solve for y in terms of x.
24. What is the relationship between the slopes of two perpendicular lines?
Answer: Two lines are perpendicular if the product of their slopes is -1. In other words, the slope of one line is the negative reciprocal of the slope of the other.
25. What is the relationship between the slopes of two parallel lines?
Answer: Two lines are parallel if they have the same slope.
26. What is a linear equation with no solution?
Answer: A linear equation with no solution occurs when the lines representing the equations are parallel and never intersect.
27. What is a consistent and inconsistent system of linear equations?
Answer: A system is consistent if it has at least one solution, and it is inconsistent if it has no solution.
28. How do you solve for the value of y in the equation 2x + 3y = 12?
Answer: To solve for y, rearrange the equation to get y on one side: 3y = 12 - 2x and then divide by 3: y = (12 - 2x) / 3.
29. What is the substitution method for solving linear equations in two variables?
Answer: The substitution method involves solving one of the equations for one variable and substituting that value into the other equation to find the second variable.
30. What is the elimination method for solving linear equations in two variables?
Answer: The elimination method involves adding or subtracting the equations to eliminate one variable, making it easier to solve for the other.
31. How do you check if the solution to a system of equations is correct?
Answer: To check if the solution is correct, substitute the values of x and y into both original equations. If both equations are satisfied, the solution is correct.
32. What does it mean when two lines intersect at one point?
Answer: When two lines intersect at one point, it means the system of linear equations has one unique solution.
33. What is the graphical representation of a system of linear equations with one solution?
Answer: The graphical representation of a system with one solution is two lines intersecting at a single point.
34. What is the graphical representation of a system of linear equations with no solution?
Answer: The graphical representation of a system with no solution is two parallel lines that do not intersect.
35. How do you solve a system of equations by graphing?
Answer: To solve by graphing, plot both equations on a graph. The point of intersection represents the solution.
36. How do you write a linear equation in two variables from a word problem?
Answer: To write a linear equation from a word problem, identify the two variables, then translate the relationships given in the problem into an equation.
37. What does it mean if the system of equations has infinite solutions?
Answer: If the system has infinite solutions, it means the two equations represent the same line and overlap at all points.
38. How do you find the x-intercept of a linear equation?
Answer: To find the x-intercept, set y equal to zero and solve for x.
39. How do you find the y-intercept of a linear equation?
Answer: To find the y-intercept, set x equal to zero and solve for y.
40. What is the solution to the system of equations 3x + 2y = 8 and 4x - y = 3?
Answer: Solve the system using substitution or elimination. The solution to this system is x = 2 and y = 1.
FAQs on RD Sharma Solutions Class 9 Maths Chapter 13
Where can I get the precise answers of RD Sharma Solutions for Class 9 Maths Chapter 13?
You can find the precise answers to RD Sharma Solutions for Class 9 Maths Chapter 13 on various educational websites like Infinity Learn and Sri Chaitanya , and other platforms that provide free or paid access to the solutions. You can also download them as PDFs for easy reference.
Name the topics discussed in RD Sharma Solutions for Class 9 Maths Chapter 13.
RD Sharma Solutions for Chapter 13 cover topics like:
Definition and basic concepts of linear equations in two variables
Graphical representation of linear equations
Solving linear equations by substitution and elimination methods
Applications of linear equations in real-life situations
Interpreting solutions to systems of linear equations
Is it necessary to follow RD Sharma Solutions for Class 9 Maths Chapter 13 while solving textbook problems?
Yes, following RD Sharma Solutions is very helpful while solving textbook problems. The solutions offer step-by-step guidance, which helps in understanding the methods of solving linear equations and aids in better problem-solving skills, especially when tackling complex problems.
How to score 100 in maths class 9?
To score 100 in Class 9 Maths, it’s important to:
Understand all the concepts thoroughly.
Solve as many practice problems as possible, especially from the RD Sharma textbook.
Take time to review each chapter and identify areas where you need more practice.
Solve previous year’s question papers and sample papers.
Stay consistent with regular revision and follow a study plan.
Is RD Sharma important for Class 9?
Yes, RD Sharma is an important resource for Class 9 Maths as it provides a clear understanding of concepts and offers a wide range of practice problems. It follows the CBSE syllabus and is one of the most trusted textbooks for building a solid foundation in mathematics.
Which is the hardest chapter in Maths Class 9?
The difficulty of chapters may vary from student to student, but many students find chapters like Coordinate Geometry, Mensuration, and Quadratic Equations to be challenging. These chapters involve a mix of concepts and require a lot of practice. However, with consistent study and practice, they can be understood and mastered.