Pair of Linear Equations in Two Variables
Kerala Board · Class 10 · Mathematics
Quick revision notes for Pair of Linear Equations in Two Variables — Kerala Board Class 10 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Linear Equations in Two Variables
- A linear equation in two variables x and y has the form ax + by + c = 0, where a, b, c are real numbers and at least one of a or b is not zero (a² + b² ≠ 0)
- The graph of a linear equation in two variables is always a straight line
- Each point (x, y) on the line represents a solution to the equation
Pair of Linear Equations and Their Solutions
- A pair of linear equations: a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0
- Solution is a pair of values (x, y) that satisfies both equations simultaneously
- Three types of solutions: unique solution, infinitely many solutions, no solution
Graphical Method
- Plot both equations as straight lines on the same coordinate system
- Intersecting lines → unique solution (point of intersection)
- Parallel lines → no solution (lines never meet)
Relationship Between Coefficients and Nature of Solutions
- Compare ratios a₁/a₂, b₁/b₂, and c₁/c₂
- If a₁/a₂ ≠ b₁/b₂ → unique solution (intersecting lines)
- If a₁/a₂ = b₁/b₂ ≠ c₁/c₂ → no solution (parallel lines)
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Sources & Official References
- Kerala Board of Public Examinations — keralapareekshabhavan.in
- 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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