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Pair of Linear Equations in Two Variables Class 10 important questions with answers PDF download
CBSE Important Questions for Class 10 Maths Pair of Linear Equations in Two Variables - 2025-26
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FAQs on CBSE Important Questions for Class 10 Maths Pair of Linear Equations in Two Variables - 2025-26
1. What types of important questions are typically asked from Chapter 3, Pair of Linear Equations in Two Variables, in the CBSE Class 10 board exams for 2025-26?
For the 2025-26 board exams, you can expect a variety of questions from this chapter, generally covering:
- 1-mark questions: Checking for consistency of a pair of linear equations or identifying the condition for a unique solution.
- 2 or 3-mark questions: Solving a pair of linear equations using the substitution or elimination method.
- 4 or 5-mark questions: These are often word problems (situational problems) that require you to first form a pair of linear equations and then solve them. Questions involving equations reducible to linear form are also considered important.
2. Which algebraic methods for solving linear equations are in the CBSE syllabus, and how do I decide which one to use in an exam?
The two primary algebraic methods in the CBSE Class 10 syllabus for 2025-26 are the Substitution Method and the Elimination Method. To choose the best method in an exam:
- Use the Substitution Method when the coefficient of one of the variables (x or y) in either equation is 1 or -1, as it makes it easy to express that variable in terms of the other.
- Use the Elimination Method when the coefficients of one variable in both equations are the same, opposite, or can be easily made so by multiplying one or both equations. This method is generally faster for more complex coefficients.
3. How can we determine the nature of solutions for a pair of linear equations algebraically without solving them?
To determine the nature of solutions for a pair of linear equations, a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, you must compare the ratios of their coefficients:
- If a₁/a₂ ≠ b₁/b₂, the system is consistent and has a unique solution (lines intersect).
- If a₁/a₂ = b₁/b₂ = c₁/c₂, the system is dependent and consistent and has infinitely many solutions (lines are coincident).
- If a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the system is inconsistent and has no solution (lines are parallel).
4. What is the importance of word problems in this chapter, and what are some common types asked in board exams?
Word problems are extremely important as they often form the high-marks questions (4 or 5 marks) and test your ability to apply concepts. Common types include:
- Problems based on ages of two people.
- Problems involving fractions (numerator and denominator).
- Questions on fixed charges and additional charges (e.g., library fees, taxi fares).
- Problems related to speed, distance, and time, especially those involving boats (upstream and downstream).
- Questions on two-digit numbers.
5. What makes a question from this chapter a HOTS (High Order Thinking Skills) question?
A question becomes a HOTS question when it requires more than direct application of a formula. In this chapter, HOTS questions often involve:
- Situations where you must find an unknown constant (like 'k') for which the system has a specific type of solution (no solution, unique, etc.).
- Complex word problems that require careful interpretation to form the correct equations.
- Problems on equations reducible to a pair of linear equations, such as those with variables in the denominator.
6. Why is checking the ratio of coefficients a crucial first step before solving a pair of linear equations?
Checking the ratio of coefficients (a₁/a₂, b₁/b₂, c₁/c₂) is a vital exam strategy because it saves significant time. It allows you to immediately identify if a system has no solution (inconsistent) or infinitely many solutions (dependent). If a system has no solution, you don't need to waste time trying to solve it using algebraic methods. This check acts as a quick diagnostic tool, which is crucial for time management in board exams.
7. What is the most common mistake students make when solving questions on 'equations reducible to a linear form'?
The most common and critical mistake is forgetting to substitute back to find the original variables. In these problems, we typically substitute expressions like 1/x with 'u' and 1/y with 'v'. After solving for 'u' and 'v', many students forget the final step of calculating 'x' and 'y' from these values (e.g., x = 1/u). Always remember to complete this final substitution to get the correct answer.
8. Can a pair of linear equations in two variables have exactly two solutions? Explain with reasoning.
No, a system of linear equations in two variables cannot have exactly two solutions. Graphically, each linear equation represents a straight line. Two straight lines can either:
- Intersect at one point: This gives a single, unique solution.
- Be parallel: They never intersect, meaning no solution.
- Be coincident: They overlap completely, resulting in infinitely many solutions.
