Assertion: Linear equations are an important topic in Class 9 Maths, which helps in solving real-life problems and understanding the concept of algebraic equations.

Reasoning: Linear equations involve the concept of variables and constants, where the variables are represented by letters and the constants are fixed values. These equations have a degree of 1, meaning the highest power of the variable is 1. Solving linear equations involves finding the value of the variable that satisfies the equation.

Explanation:

1. Introduction to Linear Equations:
Linear equations are algebraic equations that involve variables raised to the power of 1. The general form of a linear equation is represented as ax + b = 0, where 'a' and 'b' are constants and 'x' is the variable. Linear equations can have one variable or multiple variables.

2. Solving Linear Equations:
To solve a linear equation, we need to isolate the variable on one side of the equation. The goal is to determine the value of the variable that satisfies the equation. We can use various methods to solve linear equations, such as:

- Addition or subtraction method: In this method, we perform operations on both sides of the equation to eliminate one variable and solve for the other.
- Substitution method: In this method, we substitute the value of one variable from one equation into another equation to find the value of the other variable.
- Cross-multiplication method: This method is used to solve equations involving fractions. We cross-multiply the fractions to eliminate the denominators and solve for the variable.

3. Applications of Linear Equations:
Linear equations have numerous applications in real-life situations. Some of the common applications include:

- Cost and revenue problems: Linear equations can be used to determine the cost and revenue of a product or service. It helps in calculating the break-even point, profit, and loss.
- Distance and speed problems: Linear equations can be used to solve problems related to distance, speed, and time. It helps in calculating the time taken to cover a certain distance at a given speed.
- Age and number problems: Linear equations can be used to solve problems related to age and numbers. It helps in determining the present age or the number of objects.

4. Importance of Linear Equations:
Understanding linear equations is crucial as it forms the foundation for higher-level algebraic concepts. It helps in developing problem-solving skills and logical thinking. Linear equations are extensively used in various fields like engineering, economics, physics, and computer science.

In conclusion, linear equations are an essential topic in Class 9 Maths. They provide a framework for solving real-life problems and understanding the concept of algebraic equations. Mastering linear equations lays the foundation for advanced algebraic concepts and their applications in different fields.