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10th Class Mathematics Chapter – 3: PAIR OF LINEAR EQUATIONS IN TWO VARIABLES – PDF Free Download
At Ramsetu, we aim to provide educational resources that make learning engaging and comprehensive. Chapter 3, “PAIR OF LINEAR EQUATIONS IN TWO VARIABLES,” from the 10th Class Mathematics textbook, covers fundamental concepts that are essential for solving problems involving linear equations. This chapter provides students with a clear understanding of linear equations, their solutions, and their applications.
Summary of “PAIR OF LINEAR EQUATIONS IN TWO VARIABLES.”
Explanation of key concepts and properties.
Detailed examples and exercises.
Practical applications and relevance of linear equations in everyday life.
Key Concepts and Definitions:
Linear Equations: Equations of the first degree involving two variables.
Solution of Linear Equations: Values of the variables that satisfy both equations simultaneously.
Graphical Method: Solving linear equations by plotting them on a graph.
Algebraic Methods: Methods for solving linear equations algebraically, including substitution, elimination, and cross-multiplication.
Chapter Content:
Summary of “PAIR OF LINEAR EQUATIONS IN TWO VARIABLES”:
Introduction to linear equations and their graphical representation.
Methods of solving linear equations: graphical, substitution, elimination, and cross-multiplication.
Understanding the consistency and inconsistency of equations.
Key Concepts:
Graphical Method:
Plotting both equations on the same graph.
Identifying the point of intersection as the solution.
Substitution Method:
Solving one equation for one variable and substituting it into the other equation.
Elimination Method:
Adding or subtracting equations to eliminate one variable, making it easier to solve for the other.
Cross-Multiplication Method:
Using the cross-multiplication formula to solve equations directly.
Formulas and Properties:
General Form of Linear Equations: ax+by+c=0ax + by + c = 0ax+by+c=0
Consistency of Equations:
Consistent System: Has at least one solution (either unique or infinite).
Inconsistent System: Has no solution.
Types of Solutions:
Unique Solution: Lines intersect at one point.
Infinite Solutions: Lines coincide.
No Solution: Lines are parallel.
Applications:
Real-life applications of linear equations in various fields such as physics, engineering, economics, and everyday problem-solving.
Use of linear equations in constructing models and solving practical problems.
Frequently Asked Questions (FAQs):
What is a pair of linear equations in two variables?
A pair of linear equations in two variables is a set of two equations, each involving two variables, that are solved simultaneously.
How do you solve a pair of linear equations graphically?
To solve a pair of linear equations graphically, plot both equations on the same graph and identify the point where the lines intersect. This point represents the solution.
What are the algebraic methods for solving linear equations?
The algebraic methods for solving linear equations include the substitution method, elimination method, and cross-multiplication method.
