Pair of Linear Equations in Two Variables
Karnataka Board · Class 10 · Mathematics
Quick revision notes for Pair of Linear Equations in Two Variables — Karnataka Board Class 10 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
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Basic Concepts and Definitions
- A linear equation in two variables x and y has the form ax + by + c = 0, where a, b, c are real numbers and a² + b² ≠ 0
- A pair of linear equations in two variables consists of two such equations considered together
- The solution of a pair is the common solution that satisfies both equations simultaneously
Types of Solutions Based on Line Relationships
- Three possible relationships: intersecting lines (unique solution), parallel lines (no solution), coincident lines (infinite solutions)
- The relationship can be determined by comparing ratios of coefficients
- Use ratio comparison method: a₁/a₂, b₁/b₂, and c₁/c₂
Graphical Method
- Plot both equations as straight lines on coordinate plane
- Find intersection point if lines meet
- Solution is the coordinates of intersection point
Substitution Method
- Express one variable in terms of the other from either equation
- Substitute this expression into the other equation
- Solve the resulting single-variable equation
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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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