Pair of Linear Equations in Two Variables Class 10 Maths Formulas

The List of Important Formulas for Class 10 Pair of Linear Equations in Two Variables is provided on this page. We have everything covered right from basic to advanced concepts in Pair of Linear Equations in Two Variables. Make the most out of the Maths Formulas for Class 10 prepared by subject experts and take your preparation to the next level. Access the Formula Sheet of Pair of Linear Equations in Two Variables Class 10 covering numerous concepts and use them to solve your Problems effortlessly.

• 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

(i) Graphical method. The graph of a pair of linear equations in two variables is presented by two lines.
(ii) Algebraic methods. Following are the methods for finding the solutions(s) of a pair of linear equations:

• Substitution method
• Elimination method
• 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,

Relationship between coeff. or the pair of equations	Graph	Number of Solutions	Consistency of System
\(\frac { { a }_{ 1 } }{ { a }_{ 2 } } \neq \frac { { b }_{ 1 } }{ { b }_{ 2 } } \)	Intersecting lines	Unique solution	Consistent
\(\frac { { a }_{ 1 } }{ { a }_{ 2 } } =\frac { { b }_{ 1 } }{ { b }_{ 2 } } \neq \frac { c_{ 1 } }{ c_{ 2 } } \)	Parallel lines	No solution	Inconsistent
\(\frac { { a }_{ 1 } }{ { a }_{ 2 } } =\frac { { b }_{ 1 } }{ { b }_{ 2 } } =\frac { c_{ 1 } }{ c_{ 2 } } \)	Co-incident lines	Infinite solutions	Consistent