Linear Equation in Two Variables

Linear equations in two variables are equations that involve two variables, x and y, and their degree is one. Such equations can be represented by a straight line on a coordinate plane.

General Form of a Linear Equation in Two Variables

The general form of a linear equation in two variables is Ax + By + C = 0. Here, A, B, and C are constants and x and y are variables.

Solution of Linear Equations in Two Variables

The solution of a linear equation in two variables is an ordered pair of values (x, y) that satisfy the equation.

Methods of Solving Linear Equations in Two Variables

There are three methods of solving linear equations in two variables:
1. Substitution method
2. Elimination method
3. Graphical method

Substitution Method

In the substitution method, one variable is expressed in terms of the other variable in one of the equations and then substituted into the other equation. This process results in an equation with only one variable, which can be solved easily. Then the value of the other variable is found by substitution.

Elimination Method

In the elimination method, one or both equations are multiplied by constants so that one of the variables has the same coefficient in both equations, but with opposite signs. Then, the two equations are added or subtracted to eliminate one of the variables, resulting in an equation with only one variable, which can be solved easily. Then the value of the other variable is found by substitution.

Graphical Method

The graphical method involves plotting the two equations on the coordinate plane and finding the point of intersection of the two lines. The coordinates of the point of intersection represent the solution of the system of equations.

Applications of Linear Equations in Two Variables

Linear equations in two variables are used in various fields such as economics, physics, and engineering, to solve problems related to cost, profit, time, distance, velocity, and acceleration.

In conclusion, linear equations in two variables are important tools in mathematics and have a wide range of applications in various fields. It is essential to understand the general form of a linear equation in two variables, methods of solving them, and their applications.

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