Linear Equations

A linear equation is an equation that represents a straight line on a graph. In mathematics, it is one of the fundamental concepts of algebra. A linear equation consists of variables, constants, and coefficients, combined using arithmetic operations such as addition, subtraction, multiplication, and division.

General form of a linear equation:
A linear equation can be written in the general form as:
ax + by = c

Where:
- 'x' and 'y' are variables
- 'a' and 'b' are coefficients
- 'c' is a constant

Solving a linear equation:
To solve a linear equation, the goal is to find the values of the variables that make the equation true. The process involves isolating the variables on one side of the equation and simplifying the expression to determine their values.

Methods for solving linear equations:
1. Simplification: Combine like terms and apply the basic rules of arithmetic to simplify the equation.
2. Addition and subtraction: Use addition or subtraction operations to eliminate terms and isolate the variable.
3. Multiplication and division: Multiply or divide both sides of the equation by the same value to isolate the variable.
4. Graphing: Plot the equation on a graph and find the point(s) where the line intersects the x-axis or y-axis.

Applications of linear equations:
Linear equations have numerous applications in various fields, including:
- Physics: Describing motion and forces.
- Economics: Analyzing supply and demand, cost and revenue functions.
- Engineering: Modeling electrical circuits, structural analysis.
- Finance: Calculating interest rates, loan payments, and investments.
- Geometry: Finding the equation of a line, determining the intersection of lines.

Summary:
Linear equations are fundamental in algebra and represent a straight line on a graph. They consist of variables, coefficients, and constants. Solving linear equations involves isolating the variables and simplifying the expression. Linear equations have wide-ranging applications in various fields of study.