Exam-Focused MCQs on Pair of Linear Equations in Two Variables for Class 10 Maths Preparation 2025-26
FAQs on Chapter 3 MCQ Practice: Pair of Linear Equations in Two Variables (Class 10 Maths, 2025-26)
1. What are the most important topics in Chapter 3, Pair of Linear Equations in Two Variables, for the CBSE Class 10 Board Exam 2025-26?
For the Class 10 board exams, the most important topics from this chapter are:
Formulating and solving word problems: This is a high-yield area, especially questions on age, fractions, fixed charges, and speed-distance-time.
Conditions for consistency: Understanding the ratio of coefficients (a₁/a₂, b₁/b₂, c₁/c₂) to determine if a system has a unique solution, no solution, or infinitely many solutions is crucial for 1-mark and 3-mark questions.
Equations reducible to linear form: These are often considered HOTS (Higher Order Thinking Skills) questions and frequently appear as 5-mark questions.
Algebraic solving methods: Mastery of both the elimination and substitution methods is essential.
2. Which types of word problems are frequently asked as important questions from this chapter?
Based on previous CBSE board trends, you should focus on the following types of word problems:
Upstream and Downstream Problems: Involving the speed of a boat in still water and the speed of the stream.
Fixed Charge Problems: Questions related to library charges, taxi fares, or hostel fees which have a fixed component and a variable component.
Age-Related Problems: Questions comparing the present and future/past ages of two people.
Fraction Problems: Where a fraction changes based on adjustments to its numerator and denominator.
Geometry and Mensuration Problems: Questions based on the properties of triangles, rectangles (area and perimeter).
3. How are marks typically distributed for a 3-mark or 5-mark important question on solving linear equations?
In a typical CBSE evaluation for a long-answer question from this chapter, marks are distributed as follows:
Formulating the correct pair of linear equations from the given word problem: 1 mark.
Applying the correct algebraic method (elimination or substitution) and showing the steps accurately: 1 to 2 marks.
Calculating the correct final values for the variables and stating the answer with appropriate units (if any): 1 to 2 marks.
Even if your final answer is incorrect, you can still score marks for setting up the equations correctly and for the method.
4. What makes a question from this chapter a HOTS (Higher Order Thinking Skills) question?
A question on a pair of linear equations is considered a HOTS question if it involves more than just direct solving. Key factors include:
Equations Reducible to Linear Form: Problems where the variables are in the denominator (e.g., 2/x + 3/y = 13) require an initial substitution (like u = 1/x, v = 1/y) before they can be solved.
Complex Word Problems: Situations that require careful interpretation to form the two equations, often involving multiple conditions or steps, such as multi-part speed-distance problems.
Questions involving unknown constants: For instance, finding the value of 'k' for which a system of equations has no solution or infinitely many solutions.
5. Why is it important to check the conditions for consistency before solving a pair of linear equations in an exam?
Checking the ratio of coefficients (a₁/a₂, b₁/b₂, c₁/c₂) for consistency is a crucial exam strategy. It helps you quickly determine if the system has a unique solution, no solution, or infinitely many solutions. This is important because if the equations represent parallel lines (no solution), you save valuable time by not attempting to find a solution that doesn't exist. This check can also be a 1-mark question on its own.
6. In an exam, how do I decide whether to use the substitution method or the elimination method for a faster solution?
While both methods yield the correct answer, you can choose strategically to save time:
Use the substitution method when the coefficient of one of the variables (x or y) in either equation is 1 or -1. This makes it very easy to express that variable in terms of the other without creating complex fractions.
Use the elimination method when no variable has a coefficient of 1. It is generally faster for equations with larger or fractional coefficients, as you can multiply the equations by suitable numbers to make the coefficients of one variable equal or opposite.
7. What is a common mistake students make when setting up equations for upstream and downstream problems?
The most common mistake is confusing the relative speeds. Students often mix up when to add or subtract the speed of the stream. Remember the correct formulation:
Let the speed of the boat in still water be 'u' km/hr and the speed of the stream be 'v' km/hr.
Downstream speed (going with the current) = (u + v) km/hr.
Upstream speed (going against the current) = (u - v) km/hr.
Always use the formula Time = Distance / Speed with these correct relative speeds to form your equations.
8. What is the importance of the graphical representation of linear equations, even if questions often ask for an algebraic solution?
Understanding the graphical representation is fundamentally important because it provides a visual meaning to the algebraic solution. It helps you understand:
Why a system has a unique solution (the lines intersect at one point).
Why a system has no solution (the lines are parallel and never intersect).
Why a system has infinitely many solutions (the lines are coincident, or the same line).
This conceptual clarity is vital for answering objective-type and concept-based questions correctly in the board exam.
