Linear Equations in Two Variables
Maharashtra Board · Class 10 · Mathematics
Quick revision notes for Linear Equations in Two Variables — Maharashtra Board Class 10 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Basic Concepts and Definitions
- A linear equation in two variables has degree 1 for each variable term
- General form: ax + by + c = 0 where a, b, c are real numbers and a, b are not both zero
- Every solution is an ordered pair (x, y) that satisfies the equation
Graphical Method
- Graph of linear equation in two variables is a straight line
- At least 2 points needed to draw a line, but plot 3-4 points for accuracy
- Intersection point of two lines gives the solution of simultaneous equations
Determinants and Cramer's Rule
- Determinant is a number associated with a square arrangement of numbers
- 2×2 determinant |a b; c d| = ad - bc
- Cramer's rule provides a systematic method to solve simultaneous equations
Types of Solutions
- Unique solution: Two lines intersect at one point (D ≠ 0)
- Infinite solutions: Two equations represent the same line (coincident lines)
- No solution: Two lines are parallel but not coincident
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