Class 10 Maths - RAJASTHAN
Pair of Linear Equations in Two Variables
The chapter 'Pair of Linear Equations in Two Variables' in Class 10 Mathematics builds on your understanding of single linear equations by introducing two equations with two variables simultaneously. You will learn how to represent real-life situations algebraically and graphically. The chapter covers crucial methods to find solutions, including graphical, substitution, elimination, and cross-multiplication methods, along with equations reducible to linear form. This is a high-scoring unit in the Rajasthan (RBSE) board exams, frequently featuring graphical problems and word problems that test your analytical and problem-solving skills directly.
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 and Inconsistent Systems
A pair of linear equations is consistent if it has at least one solution (intersecting or coincident lines) and inconsistent if it has no solution (parallel lines).
Graphical Method
A visual way to solve equations by plotting both lines on a graph; the point of intersection gives the unique solution of the system.
Algebraic Methods of Solution
Techniques like substitution and elimination used to find exact numerical values of variables without needing to draw graphs.
Condition for Solvability
Comparing ratios a1/a2, b1/b2, and c1/c2 to determine whether the lines intersect uniquely, are parallel, or coincide.
Important Formulas
Board Exam Info
In the Rajasthan (RBSE) Class 10 Mathematics board exam, this chapter typically carries around 6 to 8 marks. Common question types include finding the value of an unknown parameter for unique/infinite/no solutions, graphical representation of equations, and translating word problems (like age, speed-distance, or fraction problems) into equations and solving them.
Frequently Asked Questions
How do I know whether to use the substitution method or elimination method?
You can use either method as both yield the same answer. However, the elimination method is generally faster and easier when coefficients are simple, while substitution works well if one variable is already isolated.
Is the graph mandatory to draw in the exam if asked?
Yes, if a question specifically asks you to solve the pair of linear equations graphically, you must draw the graph neatly on graph paper and clearly state the coordinates of the intersecting point.
What should I do if the equations are given in fraction form like 1/x and 1/y?
You should first substitute 1/x = p and 1/y = q to convert them into standard linear equations, solve for p and q, and then find the values of x and y.
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