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What is the use of pair of linear equations in two variables?
The main objective for the applications of linear equations or linear systems is to solve various problems using two variables where one is known, and the other is unknown, also dependent on the first. Some of these applications of linear equations are Geometry problems by using two variables.
How do you solve a pair of linear equations?
To solve linear equations graphically, first graph both equations in the same coordinate system and check for the intersection point in the graph. For example, take two equations as 2x + 3y = 9 and x – y = 3. Now, to plot the graph, consider x = {0. 1, 2, 3, 4} and solve for y.
What are the conditions for a linear equation in two variables?
An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.
What is the general form of a pair of linear equations?
The general form of a pair of linear equations in two variables is a 1 x + b 1 y + c 1 = 0 and a 2 x + b 2 y + c 2 = 0, where a 1, b 1, c 1, a 2, b 2, c 2 are all real numbers.
RD Sharma Solutions Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables
In this article we have provided RD Sharma Solutions Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables prepared by our experts to help students to prepare better for their examinations.
Neha Tanna15 Nov, 2024
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RD Sharma Solutions Class 10 Maths Chapter 3:
Chapter 3 of RD Sharma Class 10 Maths, "Pair of Linear Equations in Two Variables," focuses on solving linear equations with two variables, an essential topic in algebra. It introduces different methods to find solutions, including the graphical method, substitution method, elimination method, and cross-multiplication method.
The chapter covers the conditions for consistency and inconsistency of equations, along with various examples and exercises to help students master the concepts. Each method is explained with clear steps and practice problems, allowing students to understand and apply these techniques in solving real-world problems involving linear equations.
RD Sharma Solutions Class 10 Maths Chapter 3 Overview
Chapter 3 of RD Sharma’s Class 10 Maths book, Pair of Linear Equations in Two Variables, is essential for understanding how to solve and interpret two-variable linear equations. This chapter introduces methods like graphical, substitution, elimination, and cross-multiplication techniques, which are foundational for solving real-life problems involving relationships between two quantities.
By exploring these techniques, students learn to analyze, predict, and represent scenarios such as cost calculations, motion, mixtures, and age problems, enhancing logical and analytical skills. This topic is crucial not only for exams but also as a building block for advanced math and subjects like physics, economics, and engineering, where multi-variable relationships are common. Mastering these concepts prepares students for future challenges in academics and beyond.
An equation in the form ax+by+c, where a, b, and c are real numbers and a, b are not equal to zero, is called a linear equation in two variables. In a pair of linear equations in two variables, we deal with two such equations. The solution to such equations is a point on the line that represents the equation.
A two-sided statement with the same sign on both sides is called an equation. A mathematical expression with non-negative integer powers for the variables is called a polynomial. For example, whereas x3/5+ 3x0.6 is not a polynomial, x4 + 3x3 + 2x9 is. When defining polynomials, it is important to understand the idea of "degree." A degree is the largest power of the variable in the given polynomial. A polynomial of degree one is called a linear polynomial. A degree 2 polynomial is called a quadratic polynomial, while a degree 3 polynomial is called a cubic polynomial.
Representation
Two methods can be used to solve and express the pair of linear equations:
Graphical Approach
The Algebraic Approach
RD Sharma Solutions Class 10 Maths Chapter 3 PDF
Below, we have provided the PDF solutions for RD Sharma Class 10 Maths Chapter 3, "Pair of Linear Equations in Two Variables." This chapter explores methods to solve linear equations, such as substitution, elimination, and cross-multiplication, with a focus on real-life applications. These solutions will help students gain a clear understanding of the concepts and enhance their problem-solving skills in this important area of mathematics.
RD Sharma Solutions Class 10 Maths Chapter 3 Exercises
Here we have provided RD Sharma Solutions Class 10 Maths Chapter 3 to help students in their exam preparation. These solutions are created to help students understand and solve problems effectively, ensuring a strong grasp of the concepts.
Here is the RD Sharma Solutions Class 10 Maths Chapter 3 in table form:
Benefits of RD Sharma Solutions Class 10 Maths Chapter 3
Using RD Sharma Solutions for Class 10 Maths Chapter 3, which covers "Pair of Linear Equations in Two Variables," offers several benefits for students:
Clear Conceptual Understanding
: RD Sharma Solutions provide step-by-step explanations for each topic, helping students grasp complex concepts like graphical and algebraic methods for solving linear equations. This clarity lays a strong foundation for understanding higher-level algebra in future classes.
Practice with Different Methods
: The chapter explores multiple methods for solving equations, including substitution, elimination, and cross-multiplication. Practicing these methods helps students learn different approaches, increasing problem-solving flexibility and confidence.
Exam-oriented Practice
: The solutions align with the CBSE exam pattern, including important questions frequently asked in board exams. Practicing these can give students a strategic advantage in tackling similar questions in their exams.
Detailed Step-by-Step Solutions
: Each solution is broken down into detailed steps, making it easier for students to understand where they might make mistakes and how to avoid them.
Strengthens Problem-solving Skills
: Regular practice with RD Sharma Solutions helps students improve their logical thinking and problem-solving skills, which are crucial for mathematics.
Ideal for Self-study
: The solutions are designed for easy self-study, enabling students to prepare independently without needing constant guidance from a teacher.
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