Pair of Linear Equations in Two Variables
 Inconsistent, Consistent, and Dependent Pairs of Linear Equations
Let a_{1}x + b_{1}y + c_{1} = 0, a_{2}x +b_{2}y + c_{2} = 0 be a system of linear equations.
A pair of linear equations in two variables can be solved by



 Graphical method
 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 +…
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