Class 10 Maths - GUJARAT
Pair of Linear Equations in Two Variables
The chapter 'Pair of Linear Equations in Two Variables' in Class 10 Gujarat (GSEB) Mathematics builds upon your foundational knowledge of linear equations. It explores graphical and algebraic methods to find the common solution for two variables simultaneously. You will learn techniques such as substitution, elimination, and cross-multiplication, alongside graphical representation to determine if lines are intersecting, parallel, or coincident. This chapter is extremely crucial for GSEB board exams as it consistently features in multi-mark descriptive questions and forms the base for word problems that test your practical application skills.
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, representing a straight line on a graph.
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 technique to solve equations by plotting both lines on a Cartesian plane; the point of intersection represents the unique solution.
Algebraic Methods
Methods like Substitution and Elimination used to find precise numerical values of variables without relying on graph paper accuracy.
Condition for Solvability
Comparing ratios a1/a2, b1/b2, and c1/c2 to determine without solving whether a pair has a unique solution, infinitely many solutions, or no solution.
Important Formulas
Board Exam Info
In the Gujarat (GSEB) Class 10 Mathematics board exam, this chapter typically carries around 6 to 8 marks. Questions usually include 1-mark objective/MCQ questions, 2-mark short answer questions based on consistency ratios, and 3-to-4-mark long answer questions involving algebraic methods or word problems like age-related and speed-distance problems.
Frequently Asked Questions
How do I know which algebraic method to use in the exam?
Unless the question specifies 'solve by substitution' or 'elimination', you can use whichever method you find faster and more accurate. Elimination is generally preferred by students for its speed.
What should I do if the graph lines are parallel?
If the graphical representation yields parallel lines, state clearly that the pair of equations is inconsistent and has no solution.
How do I convert a word problem into linear equations?
Read the problem carefully, assign variables like x and y to the two unknown quantities, frame two distinct equations based on the given conditions, and then apply any solving method.
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