Class 10 Algebra (Part 1) – Chapter 1:
Linear Equations in Two Variables
1. General Form of Linear Equation
A linear equation in two variables can be written as:
ax + by + c = 0
Where:
- x and y are variables
- a, b, and c are real numbers
- a ≠ 0 or b ≠ 0
2. Solution of Linear Equation
A solution is a pair of values (x, y) that satisfies the equation.
Every linear equation has infinite solutions.
3. Graph of Linear Equation
The graph is a straight line.
To draw:
1. Choose any two values of x
2. Find corresponding y
3. Plot the points and join
4. Pair of Linear Equations (Simultaneous Equations)
Two equations:
a₁x + b₁y = c₁
a₂x + b₂y = c₂
These are solved to find a common solution (x, y).
5. Methods to Solve Pair of Linear Equations
A. Substitution Method:
1. Express one variable in terms of the other using one equation
2. Substitute into the second equation
3. Solve and find both values
Linear Equations in Two Variables
1. General Form of Linear Equation
A linear equation in two variables can be written as:
ax + by + c = 0
Where:
- x and y are variables
- a, b, and c are real numbers
- a ≠ 0 or b ≠ 0
2. Solution of Linear Equation
A solution is a pair of values (x, y) that satisfies the equation.
Every linear equation has infinite solutions.
3. Graph of Linear Equation
The graph is a straight line.
To draw:
1. Choose any two values of x
2. Find corresponding y
3. Plot the points and join
4. Pair of Linear Equations (Simultaneous Equations)
Two equations:
a₁x + b₁y = c₁
a₂x + b₂y = c₂
These are solved to find a common solution (x, y).
5. Methods to Solve Pair of Linear Equations
A. Substitution Method:
1. Express one variable in terms of the other using one equation
2. Substitute into the second equation
3. Solve and find both values
