Class 10 Maths - BIHAR
Pair of Linear Equations in Two Variables
The chapter 'Pair of Linear Equations in Two Variables' in Class 10 Bihar Board Mathematics builds upon foundational algebra by introducing systems of two linear equations. Students learn to represent real-life situations mathematically and solve them using algebraic methods like substitution and elimination, as well as the graphical method. This chapter is highly scoring in the BSEB Matric examination and forms the backbone for solving word problems related to age, speed-distance, and fractions. Mastering consistency conditions and cross-multiplication or elimination techniques is crucial for securing top marks in both objective and subjective sections.
Start Learning FreeKey Concepts
Linear Equation in Two Variables
An equation of the form ax + by + c = 0, where a, b, and c are real numbers and a, b are not both zero, is called a linear equation in two variables.
Graphical Representation
The graph of a pair of linear equations in two variables is always represented by two straight lines, which can intersect, be parallel, or coincide.
Consistent and Inconsistent Systems
A pair of linear equations with at least one solution is called consistent, while a pair with no solution is called inconsistent.
Algebraic Methods of Solution
Techniques such as the Substitution Method and the Elimination Method used to find the exact numerical values of the two variables satisfying both equations.
Conditions for Solvability
For equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, unique solution occurs when (a1/a2) ≠ (b1/b2), infinitely many solutions when (a1/a2) = (b1/b2) = (c1/c2), and no solution when (a1/a2) = (b1/b2) ≠ (c1/c2).
Important Formulas
Board Exam Info
In the Bihar School Examination Board (BSEB) Class 10 Mathematics exam, this chapter typically carries around 6 to 8 marks. Questions frequently appear as multiple-choice questions (MCQs) checking consistency conditions, 2-mark short answer questions solving equations using substitution or elimination, and a 5-mark long answer question based on word problems or graphical representation.
Frequently Asked Questions
How do I know if a pair of linear equations has a unique solution?
You compare the ratios of the coefficients of x and y. If a1/a2 is not equal to b1/b2, the system has a unique solution.
Can I use any method to solve the equations in the BSEB exam unless specified?
Yes, unless the question specifically asks you to use the graphical method or a particular algebraic method, you can use whichever method you find easiest, usually elimination or substitution.
What does a pair of parallel lines on a graph indicate about the equations?
Parallel lines indicate that the equations have no common solution, meaning the system is inconsistent.
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