Linear Equations in Two Variables

Definition:
A linear equation in two variables is an equation that can be written in the form ax + by = c, where a, b, and c are constants and x and y are variables. The graph of a linear equation in two variables is a straight line.

Examples of Linear Equations in Two Variables:

1. 2x + 3y = 7:
- In this equation, the coefficients of x and y are 2 and 3, respectively.
- The constant term is 7.
- The equation represents a straight line.

2. 5x - 2y = 10:
- The coefficient of x is 5, and the coefficient of y is -2.
- The constant term is 10.
- The equation represents a straight line.

3. -3x + 4y = -12:
- The coefficient of x is -3, and the coefficient of y is 4.
- The constant term is -12.
- The equation represents a straight line.

4. x + y = 5:
- The coefficient of x is 1, and the coefficient of y is 1.
- The constant term is 5.
- The equation represents a straight line.

5. 2x - 7y = 3:
- The coefficient of x is 2, and the coefficient of y is -7.
- The constant term is 3.
- The equation represents a straight line.

Graphical Representation:
The graph of a linear equation in two variables is a straight line. To graph a linear equation, we can plot a few points and then connect them to form a line. Each point on the line satisfies the equation.

Interpretation:
In the context of real-life situations, linear equations in two variables can represent various scenarios. For example:
- The cost of buying x apples and y oranges can be represented by a linear equation.
- The distance traveled by a car at a certain speed and time can be represented by a linear equation.

Summary:
- A linear equation in two variables is an equation that can be written in the form ax + by = c.
- It represents a straight line on a graph.
- The coefficients of x and y determine the slope of the line.
- The constant term represents the y-intercept of the line.
- Linear equations in two variables can be used to model real-life situations.