Chapter 3: Pair of Linear Equations in Two Variables
Understanding and Representing Linear Equations
Linear equations in two variables, like ax+by+c=0, can represent real-world situations such as spending money at a fair or comparing quantities. These equations form straight lines when plotted on a graph. A pair of linear equations can have one solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (coincident lines). The nature of the solution depends on comparing the ratios of the coefficients of the variables.
Methods of Solving Pairs of Linear Equations
Three main methods are used:
- Graphical Method: Plot both equations and find their intersection point(s).
- Substitution Method: Solve one equation for a variable and substitute it into the other.
- Elimination Method: Eliminate one variable by adding or subtracting the equations after suitable multiplication. These algebraic methods are especially useful when graphing is impractical due to decimal or fractional answers.
Real-Life Applications and Summary
The chapter includes word problems that convert real situations into pairs of linear equations—such as calculating costs, ages, or distances. Students learn how to form equations from given information and solve them using a suitable method. A summary at the end recaps conditions for consistency, dependence, and types of solutions, reinforcing both the conceptual and procedural understanding of solving such equatDeepak Bhatt