Pair of Linear Equations in Two Variables Class 10 Mathematics — Revision Notes
Pairs of linear equations can be solved using multiple methods to find values of two unknowns. Understanding graphical and algebraic methods helps solve re
TL;DR: Pairs of linear equations can be solved using multiple methods to find values of two unknowns. Understanding graphical and algebraic methods helps sol…
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Pairs of linear equations can be solved using multiple methods to find values of two unknowns. Understanding graphical and algebraic methods helps solve re
Representation of Linear Equations
- Linear equation: ax + by + c = 0 where a, b, c are constants and a, b not both zero
- General form: a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0
- Graphically: straight line on coordinate plane
Types of Solutions
- Unique solution: lines intersect at one point when a1/a2 ≠ b1/b2 (consistent and independent)
- Infinite solutions: coincident lines when a1/a2 = b1/b2 = c1/c2 (consistent and dependent)
- No solution: parallel lines when a1/a2 = b1/b2 but ≠ c1/c2 (inconsistent)
Algebraic Methods of Solution
- Substitution method: express one variable in terms of other, substitute in second equation
- Elimination method: make coefficients equal, add or subtract to eliminate variable
- Cross-multiplication method: uses formula for quick solution
Graphical Method
- Plot both lines on coordinate plane
- Point of intersection gives solution
- Parallel lines indicate no solution, coincident lines indicate infinite solutions
Key Terms
- Linear Equation: Equation of degree 1 with variables, graph is straight line
- Consistent Equations: System with at least one solution
- Inconsistent Equations: System with no solution
- Dependent Equations: Equations representing same line (infinite solutions)
- Independent Equations: Equations representing different lines
Frequently Asked Questions
How do you determine if a system has unique, infinite, or no solution without solving?
Check ratios: a1/a2 ≠ b1/b2 (unique), a1/a2 = b1/b2 = c1/c2 (infinite), a1/a2 = b1/b2 ≠ c1/c2 (no solution).
When should you use elimination method vs substitution method?
Use elimination when coefficients align easily; use substitution when one variable has coefficient 1.
Can a pair of linear equations have exactly two solutions?
No, a pair of linear equations can have either unique solution, infinite solutions, or no solution.
More Class 10 Mathematics Revision Notes
- Real Numbers
- Polynomials
- Pair of Linear Equations in Two Variables
- Quadratic Equations
- Arithmetic Progressions
- Triangles
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