Class 10 Maths - ODISHA
Pair of Linear Equations in Two Variables
The chapter 'Pair of Linear Equations in Two Variables' in Class 10 Mathematics for BSE Odisha builds on your knowledge of single-variable equations. It introduces you to systems of two linear equations that represent straight lines on a Cartesian plane. You will learn how to find their common solution using graphical methods as well as algebraic methods like substitution, elimination, and cross-multiplication. This chapter is fundamental for mastering coordinate geometry and algebra, and it carries significant weight in the BSE Odisha board examinations through short-answer and long-answer problem-solving questions.
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, whose graph is always a straight line.
Consistent System
A pair of linear equations that has at least one solution (either unique or infinitely many solutions).
Inconsistent System
A pair of linear equations that has no solution, represented graphically by parallel lines.
Graphical Method
Finding the solution of a pair of equations by plotting their lines on a graph and identifying their point of intersection.
Algebraic Methods
Techniques such as Substitution, Elimination, and Cross-Multiplication used to calculate exact numerical solutions without drawing graphs.
Important Formulas
Board Exam Info
In the BSE Odisha Class 10 Mathematics board exam, this chapter typically carries around 6 to 8 marks. Questions usually include objective-type multiple-choice questions (MCQs), 2-mark short answer questions based on checking consistency ratios, and 4-mark long answer questions requiring students to solve word problems or simultaneous equations using algebraic methods.
Frequently Asked Questions
How do I know if a pair of equations has a unique solution?
Compare the coefficients of x and y. If a1/a2 is not equal to b1/b2, the lines intersect at one point and have a unique solution.
Which method is best to solve word problems in this chapter?
The Elimination method is generally the fastest and easiest to apply after setting up the two linear equations from the word problem.
Is graph plotting mandatory in the board exam for this chapter?
Yes, a 5-mark or 4-mark question requiring you to solve a pair of linear equations graphically may occasionally appear, so practicing graph construction is essential.
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