3.7 SUMMARY:

In this chapter, you have studied the following points:

- Two linear equations in the same two variables are called a pair of linear equations in two variables. The most general form of a pair of linear equations is

- A pair of linear equations in two variables can be represented,and solved,by the:
- Graphical method 2. Algebraic method

The graph of a pair of linear equations in two variables is represented by two lines.

- If the lines intersect at a point, then that point gives the unique solution of the two equations. In this case, the pair of equations is
**consistent**. - If the lines coincide,then there are infinitely many solutions—each point on the line being a solution .In this case,the pair of equations is
**dependent( consistent )**. - If the lines are parallel, then the pair of equations has no solution .In this case,the pair of equations is
**inconsistent**.

Algebraic Methods: We have discussed the following methods for finding the solution ( s ) of a pair of linear equations:

- Substitution Method
- Elimination Method
- Cross – multiplication Method

- A pair of linear equations in two variables can be represented,and solved,by the: