Class 10 Maths – Linear Equations in Two Variables Complete Notes (NCER

Class 10 Mathematics
Chapter: Linear Equations in Two Variables


1. Introduction
Linear Equation in Two Variables is an equation having two variables (x and y)
where the highest power of variables is 1.

General Form: ax + by + c = 0
Where a, b, c are constants and x, y are variables.

2. Examples
2x + 3y = 6
x-y=2
4x + 5y - 10 = 0

3. Solution of Linear Equation
The values of x and y that satisfy the equation are called its solution.

Example:
2x + y = 5
If x = 2
2(2) + y = 5
4+y=5
y=1
So (2,1) is a solution.

4. Graphical Representation
The graph of a linear equation is always a straight line.

Steps to draw graph:
1) Find two solutions of the equation.
2) Plot the points on graph paper.
3) Join them to form a straight line.

5. Important Facts
- Graph of linear equation is always a straight line.
- If two lines intersect at one point, there is one solution.
- If two lines coincide, there are infinite solutions.
- If two lines are parallel, there is no solution.

6. Practice Questions
1) Find one solution of 3x + 2y = 12.
2) Find two solutions of 2x - y = 4.
3) Write the general form of linear equation.
4) Draw the graph of x + y = 10.

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