Hello Adityaraj

Main Concepts of finding the roots are-

• Two linear equations in the same two variables are said to form a pair of linear
equations in two variables.

• The most general form of a pair of linear equations is
a1x + b1 y + c1= 0
a2x + b2 y + c2= 0,
where a1, a2, b1, b2, c1, c2 are real numbers, such that 22 22
11 22 ab ab + ≠ +≠ 0, 0 .

• A pair of linear equations is consistent if it has a solution – either a unique or
infinitely many.
In case of infinitely many solutions, the pair of linear equations is also said to be
dependent. Thus, in this case, the pair of linear equations is dependent and consistent.
• A pair of linear equations is inconsistent, if it has no solution.