CBSE Class 10 Mathematics (Standard) Chapter 3 Pair of Linear Equations in Two Variables Important Questions 2027
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17 questions from Pair of Linear Equations in Two Variables appeared in 6 of the 7 CBSE papers we analysed (2022–2026) — here are the topics that matter, the questions that repeat, and every previous-year question from this chapter.
Key facts
- Algebra unit — 20 marks in the official syllabus
- Asked in 6 of 7 analysed papers (2022–2026)
- About 2.4 questions per paper (OR alternatives counted separately)
- 2 question patterns repeated across papers
Important topics in Pair of Linear Equations in Two Variables
| # | Topic | Asked in | Importance |
|---|---|---|---|
| 1 | Graphical solution of a pair of linear equations | Board 2023Board 2024Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| 2 | Word problems on pair of linear equations | Board 2023Board 2024Board 2025Sample 2025Sample 2026 | ★★☆☆☆ |
| 3 | Consistency / number of solutions from coefficients | Board 2023Board 2026Sample 2025Sample 2026 | ★☆☆☆☆ |
| 4 | Solving by substitution method | Board 2025 | ★☆☆☆☆ |
| 5 | Solving by elimination method | Board 2024 | ★☆☆☆☆ |
Repeated questions from Pair of Linear Equations in Two Variables
1. Solve a pair graphically
3×Board 2026Sample 2025Sample 20263/5 marks
Aarush bought 2 pencils and 3 chocolates for Rs 11 and Tanish bought 1 pencil and 2 chocolates for Rs 7 from the same shop. Represent this situation in the form of a pair of linear equations. Find the price of 1 pencil and 1 chocolate, graphically.
2. Find k from coefficient-ratio conditions
3×Board 2023Sample 2025Sample 20261 marks
If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are not parallel, then k has to be (A) 15/4 (B) not equal to 15/4 (C) any rational number (D) any rational number having 4 as denominator
Pair of Linear Equations in Two Variables questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 0 | 0 |
| Board 2023 | 4 | 8 |
| Board 2024 | 3 | 6 |
| Board 2025 | 2 | 6 |
| Sample 2025 | 3 | 11 |
| Board 2026 | 2 | 6 |
| Sample 2026 | 3 | 7 |
Counts include both options of internal-choice (OR) questions.
Previous year questions: Pair of Linear Equations in Two Variables
Board 2026 2 questions
If the pair of linear equations : a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 is consistent and dependent, then (A) a1/a2 != b1/b2 (B) a1/a2 != b1/b2 = c1/c2 (C) a1/a2 = b1/b2 != c1/c2 (D) a1/a2 = b1/b2 = c1/c2
Aarush bought 2 pencils and 3 chocolates for Rs 11 and Tanish bought 1 pencil and 2 chocolates for Rs 7 from the same shop. Represent this situation in the form of a pair of linear equations. Find the price of 1 pencil and 1 chocolate, graphically.
Sample 2026 3 questions
If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are not parallel, then k has to be (A) 15/4 (B) not equal to 15/4 (C) any rational number (D) any rational number having 4 as denominator
The monthly income of Aryan and Babban are in the ratio 3:4 and their monthly expenditures are in ratio 5:7. If each saves Rs 15,000 per month, find their monthly incomes.
Solve the following system of equations graphically: 2x + y = 6, 2x - y - 2 = 0. Find the area of the triangle so formed by two lines and x-axis. [For Visually Impaired candidates: Five years hence, father's age will be three times the age of son. Five years ago, father was seven times as old as his son. Find their present ages.]
Board 2025 2 questions
If x = 1 and y = 2 is a solution of the pair of linear equations 2x - 3y + a = 0 and 2x + 3y - b = 0, then : (A) a = 2b (B) 2a = b (C) a + 2b = 0 (D) 2a + b = 0
Vijay invested certain amounts of money in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum, respectively. He received Rs 1,860 as the total annual interest. However, had he interchanged the amounts of investments in the two schemes, he would have received Rs 20 more as annual interest. How much money did he invest in each scheme ?
Sample 2025 3 questions
The value of k for which the system of equations 3x-ky=7 and 6x+10y=3 is inconsistent, is A) -10 B) -5 C) 5 D) 7
Solve the following system of linear equations graphically: x+2y = 3, 2x-3y+8 = 0
Places A and B are 180 km apart on a highway. One car starts from A and another from B at the same time. If the car travels in the same direction at different speeds, they meet in 9 hours. If they travel towards each other with the same speeds as before, they meet in an hour. What are the speeds of the two cars?
Board 2024 3 questions
In the given figure, graphs of two linear equations are shown (two lines intersecting at a point). The pair of these linear equations is: (a) consistent with unique solution. (b) consistent with infinitely many solutions. (c) inconsistent. (d) inconsistent but can be made consistent by extending these lines.
Solve the following system of linear equations 7x - 2y = 5 and 8x + 7y = 15 and verify your answer.
Three years ago, Rashmi was thrice as old as Nazma. Ten years later, Rashmi will be twice as old as Nazma. How old are Rashmi and Nazma now?
Board 2023 4 questions
The value of k for which the pair of equations kx = y + 2 and 6x = 2y + 3 has infinitely many solutions, (A) is k = 3 (B) does not exist (C) is k = -3 (D) is k = 4
Solve the pair of equations x = 3 and y = -4 graphically.
Using graphical method, find whether following system of linear equations is consistent or not: x = 0 and y = -7
Half of the difference between two numbers is 2. The sum of the greater number and twice the smaller number is 13. Find the numbers.
Frequently asked questions
What are the most important topics in CBSE Class 10 Mathematics (Standard) Chapter 3 Pair of Linear Equations in Two Variables?
By how often and how recently they were asked: Graphical solution of a pair of linear equations; Word problems on pair of linear equations; Consistency / number of solutions from coefficients.
How many marks does Pair of Linear Equations in Two Variables carry in the CBSE Class 10 Mathematics (Standard) exam?
Pair of Linear Equations in Two Variables is part of the Algebra unit, which carries 20 marks in the official syllabus. In the analysed papers it had about 2.4 questions per paper.
Do questions from Pair of Linear Equations in Two Variables repeat in board exams?
Yes — 2 question patterns from this chapter appeared in two or more past board or official sample papers. They are listed on this page with the years they were asked.