In Class 7 Mathematics (ICSE), linear equations are an important topic. Here’s a summary:

1. **Introduction to Linear Equations:** Linear equations are equations of the form (ax + b = 0), where (a) and (b) are constants, and (x) is the variable. Solving a linear equation means finding the value of (x) that satisfies the equation.

2. **Methods of Solving Linear Equations:** There are several methods to solve linear equations, including the method of balancing (addition and subtraction), the method of transposition (moving terms to the other side), and the method of cross multiplication.

3. **Applications of Linear Equations:** Linear equations are used to solve various real-life problems, such as finding the cost of items, determining the time taken to complete a task, or calculating the speed of an object.

4. **Graphical Representation:** Linear equations can be represented graphically as straight lines on a graph. The slope-intercept form (y = mx + c) is often used to represent linear equations, where (m) is the slope and (c) is the y-intercept.

5. **Word Problems:** Linear equations are commonly used to solve word problems involving proportions, rates, distances, and mixtures.

6. **Practice and Application:** Practice is key to mastering linear equations. Solving a variety of problems and understanding the concepts thoroughly will help in applying them effectively in different scenarios.

It’s important to understand the basics of linear equations as they form the foundation for more advanced topics in mathematics.