Maths Class 10 Chapter 3: Pair of Linear Equations in Two Variables

# Maths Class 10 Chapter 3: Pair of Linear Equations in Two Variables

Important Concepts and Formulas

1.      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
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
where a1, a2, b1, b2, c1, c2 are real numbers such that a12 + b12 0 and a22 + b22 0.

2.      A pair of linear equations in two variables can be represented and solved by the following methods:
i.            Graphical method
ii.            Algebraic method

3.      Graphical method: The graph of a pair of linear equations in two variables is represented by two lines.
i.            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.
ii.            If the lines coincide, then there are infinitely many solutions, i.e., each point on the line being a solution. In this case, the pair the equations is dependent (consistent).
iii.            If the lines are parallel, then the pair of equations has no solution. In this case, the pair of equations is inconsistent.

4.      Algebraic method: We use the following methods to find the solution of a pair of linear equations:
i.

ii.

iii.