Class 10 Maths - CBSE
Pair of Linear Equations in Two Variables
The chapter 'Pair of Linear Equations in Two Variables' builds upon your previous knowledge of linear equations by introducing systems of two equations solved simultaneously. You will learn algebraic methods like substitution and elimination, alongside graphical representations to understand consistency and dependency of equations. This topic is fundamental for the CBSE Class 10 board exams as it tests both calculation accuracy and logical reasoning. Mastering this chapter ensures you can solve word problems involving ages, speeds, and fractions, which frequently appear in board papers and form the basis for higher-level mathematics.
Start Learning FreeKey Concepts
General Form
A pair of linear equations in two variables, x and y, is written as a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, where a1, b1, c1, a2, b2, c2 are real numbers and a1^2 + b1^2 ≠ 0 and a2^2 + b2^2 ≠ 0.
Consistent vs Inconsistent Systems
A system is consistent if it has at least one solution (intersecting or coincident lines) and inconsistent if it has no solution (parallel lines).
Graphical Method
Plotting both equations on a graph yields two lines; their point of intersection represents the unique solution to the system.
Substitution Method
Solving one equation for one variable and substituting that expression into the other equation to find the value of the remaining variable.
Elimination Method
Multiplying equations by suitable constants to make the coefficients of one variable equal, then adding or subtracting to eliminate that variable.
Important Formulas
Board Exam Info
In the CBSE Class 10 Mathematics board exam, this chapter typically carries around 6 to 8 marks. Questions commonly include 1-mark multiple-choice questions on consistency conditions, 2-mark or 3-mark questions on algebraic solving methods (substitution/elimination), and a 5-mark long-answer question based on a real-world word problem.
Frequently Asked Questions
How do I know which algebraic method to use in the exam?
Unless the question specifies a method like substitution or elimination, you can use whichever method you find faster and more comfortable, though elimination is often quickest for standard equations.
What does a 'dependent pair of linear equations' mean?
It means the two equations represent the exact same line on a graph, resulting in infinitely many solutions where every point on the line is a solution.
How should I approach word problems in this chapter?
First, clearly define your two variables (e.g., let age of father be x and son be y). Then, translate the sentence clues step-by-step into two separate algebraic equations before solving.
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