# NCERT Notes for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables

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

 Chapter Name Pair of Linear Equations in Two Variables Notes Class CBSE Class 10 Textbook Name NCERT Mathematics Class 10 Related Readings Notes for Class 10Notes for Class 10 MathsRevision Notes for Pair of Linear Equations in Two Variables
• For any linear equation, each solution (x, y) corresponds to a point on the line. General form is given by ax + by + c = 0.
• The graph of a linear equation is a straight line.
• 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 and c2 are real numbers, such that a12 + b12 ≠ 0, a22 + b22 ≠ 0.
• A pair of values of variables ‘x‘ and ‘y’ which satisfy both the equations in the given system of equations is said to be a solution of the simultaneous pair of linear equations.
• A pair of linear equations in two variables can be represented and solved, by
(i) Graphical method
(ii) Algebraic method

### Graphical method

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

### Algebraic methods

• Following are the methods for finding the solutions(s) of a pair of linear equations:
1. Substitution method
2. Elimination method
3. Cross-multiplication method.
• There are several situations which can be mathematically represented by two equations that are not linear to start with. But we allow them so that they are reduced to a pair of linear equations.

#### Consistent system

• A system of linear equations is said to be consistent if it has at least one solution.

#### Inconsistent system

• A system of linear equations is said to be inconsistent if it has no solution.

#### Conditions for Consistency

Let the two equations be:
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
Then,