Pair of Linear Equations in Two Variables

• Inconsistent, Consistent, and Dependent Pairs of Linear Equations

Let a₁x + b₁y + c₁ = 0, a₂x +b₂y + c₂ = 0 be a system of linear equations.

A pair of linear equations in two variables can be solved by

1. 1. 1. 1. Graphical method
         2. Algebraic method

 

• Algebraic method to solve linear equations

Case (i)         

In this case, the given system is consistent.

This implies that the system has a unique solution.

 

Case (ii)       

In this case, the given system is inconsistent.

This implies that the system has no solution.

 

Case (iii)      

In this case, the given system is dependent and consistent.

This implies that the system has infinitely many solutions.

 

Example:

Find whether the following pairs of linear equations have unique solutions, no solutions, or infinitely many solutions?

 

• • • 7x + 2y + 8 = 0

14x + 4y + 16 = 0

• • • 2x + 3y – 10 =0

5x – 2y – 6 = 0

• • • 3x – 8y + 12 = 0

6x – 16y + 14 = 0

 

Solution:

 

• • • 7x + 2y + 8 = 0

14x +…