Скачать или смотреть NCERT Exercise 3.2 solutions for class 10 (pair of linear equations in two variables)

In this video I have solved exercise 3.2 of your ncert book for grade 10.

In this video I have explained the basic concepts of the chapter 3 of your ncert book for grade 10.
A pair of linear equations in two variables consists of two linear equations, each involving two variables (usually x and y). These equations are called simultaneous linear equations because you are looking for values of x and y that satisfy both equations simultaneously.

Geometric Interpretation:
When you graph the two equations on the coordinate plane, each equation represents a straight line. The solution to the system is the point where the two lines intersect. This point represents the values of x and y that satisfy both equations.

Types of Solutions:
There are three possible outcomes when solving a pair of linear equations:
One unique solution: This happens when the two lines intersect at exactly one point. The system is consistent and independent.
No solution: This happens when the two lines are parallel and never intersect. The system is inconsistent.
Infinite solutions: This happens when the two lines are the same (i.e., they overlap completely). The system is consistent and dependent.

Methods to Solve a Pair of Linear Equations:
There are three common methods to solve a pair of linear equations:
1. Graphical Method:
Plot both equations on a graph.
The point where the lines intersect is the solution to the system.
2. Substitution Method:
Solve one of the equations for one variable (either xxx or yyy).
Substitute this value into the second equation and solve for the other variable.
Then substitute the value of the second variable back into the first equation to find the first variable.
3. Elimination Method (also called Addition/Subtraction Method):
Multiply the equations if necessary to make the coefficients of one of the variables the same (or opposites).
Add or subtract the equations to eliminate one variable.
Solve for the remaining variable, then substitute back to find the other variable.

Special Cases:
Parallel Lines (No Solution): If the two equations represent parallel lines, they have no point of intersection, and the system has no solution.
Coincident Lines (Infinite Solutions): If the two equations represent the same line (i.e., they are dependent), then there are infinite solutions.

Summary of Solution Types:
One unique solution: The lines intersect at one point.
No solution: The lines are parallel and never intersect.
Infinite solutions: The lines coincide (overlap completely).

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