Linear Equations in Two Variables
Gujarat Board · Class 9 · Mathematics
Quick revision notes for Linear Equations in Two Variables — Gujarat Board Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
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Introduction to Linear Equations in Two Variables
- A linear equation in one variable has a unique solution (e.g., x + 1 = 0 has solution x = -1)
- Linear equations in two variables involve two unknown quantities, typically denoted as x and y
- Real-life situations often involve two unknowns, making linear equations in two variables essential
Converting Equations to Standard Form
- Any linear equation can be written in the form ax + by + c = 0
- Equations like x = -5 become 1·x + 0·y + 5 = 0
- Equations like y = 2 become 0·x + 1·y - 2 = 0
Solutions of Linear Equations in Two Variables
- A solution is an ordered pair (x, y) that satisfies the equation
- Linear equations in two variables have infinitely many solutions
- Solutions are written as ordered pairs: (x-value, y-value)
Special Cases and Examples
- Equations like 2x + 5y = 0 pass through origin (0, 0)
- Equations like 3y + 4 = 0 represent horizontal lines (y = constant)
- Equations like 2x - 7 = 0 represent vertical lines (x = constant)
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