Class 10 · Chapter 3
Pair of Linear Equations in Two Variables
Graphical and algebraic methods (substitution, elimination, cross-multiplication) to solve two linear equations in two variables.
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Detailed theory
Each equation represents a straight line. Two lines can (i) intersect at one point — unique solution (consistent, independent), (ii) be coincident — infinitely many solutions (consistent, dependent), (iii) be parallel — no solution (inconsistent). The relation between coefficients tells you which case.
Key concepts & formulas
01
System is consistent if it has a solution; inconsistent otherwise.
02
Unique solution: .
03
Infinitely many: .
04
No solution: .
05
Two variables need two independent equations to fix a unique point.
06
Graph of each equation is a straight line.