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Mathematics

Pair of Linear Equations in Two Variables

दो चरों वाले रैखिक समीकरणों के युग्म

In Class 10 Mathematics, the chapter Pair of Linear Equations in Two Variables introduces two linear equations considered together and the solutions that satisfy both. Students learn to represent equations graphically, interpret the intersection of lines, and determine whether a pair has one solution, no solution, or infinitely many solutions. The chapter also develops algebraic solution techniques through substitution and elimination methods for solving practical and numerical problems.

1

Graphical method of finding solutions.

ग्राफीय विधि से हल ज्ञात करना

In this Class 10 Mathematics topic from the chapter Pair of Linear Equations in Two Variables, students learn to represent each linear equation as a straight line on the Cartesian plane and identify the solution through the point where the lines intersect. The topic explains how intersecting, parallel, and coincident lines correspond to a unique solution, no solution, or infinitely many solutions. Students also practise plotting points, reading coordinates, and checking solutions graphically.

580 questions
2

Algebraic methods: Substitution method and Elimination method.

बीजीय विधियाँ: प्रतिस्थापन विधि और विलोपन विधि

This Class 10 Mathematics topic from the chapter Pair of Linear Equations in Two Variables explains two systematic ways to solve a pair of simultaneous linear equations: the substitution method and the elimination method. Students learn how to rearrange an equation, substitute an expression into the other equation, and eliminate a variable by adding, subtracting, or multiplying equations suitably. They also practise checking solutions and interpreting the ordered pair that satisfies both equations.

594 questions
3

Conditions for solvability

युग्म रैखिक समीकरणों के हल की शर्तें

In this Class 10 Mathematics topic, students learn how to determine whether a pair of linear equations in two variables has a solution. They compare the ratios of the coefficients and constants to identify the three possibilities: a unique solution, infinitely many solutions, or no solution. The topic connects algebraic conditions with the graphical meaning of intersecting, coincident, and parallel lines, helping students classify equation pairs accurately and understand when they are consistent or inconsistent.

626 questions