CBSE Class 10 Mathematics (Basic) Chapter 3 Pair of Linear Equations in Two Variables Important Questions 2027
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21 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 3.0 questions per paper (OR alternatives counted separately)
- 5 question patterns repeated across papers
Important topics in Pair of Linear Equations in Two Variables
| # | Topic | Asked in | Importance |
|---|---|---|---|
| 1 | Word problems on pair of linear equations | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| 2 | Graphical solution of a pair of linear equations | Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★☆☆☆☆ |
| 3 | Solving by elimination method | Board 2023Board 2025Board 2026Sample 2026 | ★☆☆☆☆ |
| 4 | Consistency / number of solutions from coefficients | Board 2023Board 2024Board 2025Board 2026 | ★☆☆☆☆ |
| 5 | Solving by substitution method | Board 2024 | ★☆☆☆☆ |
Repeated questions from Pair of Linear Equations in Two Variables
1. Solve graphically
3×Board 2025Board 2026Sample 20263 marks
Solve the following system of equations graphically : x + 3y = 6; 2x – 3y = 12
2. AR: consistency via ratios
3×Board 2023Board 2025Board 20261 marks
Assertion (A) : The value of p for which the system of equations 4x + py + 8 = 0 and 2x + 2y + 2 = 0 is consistent is 4. Reason (R) : The system of equations a1x + b1y = c1 and a2x + b2y = c2 is consistent with infinitely many solutions, if a1/a2 = b1/b2 = c1/c2. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Assertion (A) is false, but Reason (R) is true.
3. Solve pair by elimination
3×Board 2023Board 2025Board 20262 marks
Solve the following system of equations for x and y : x/2 + 2y/3 = – 1 and x – y/3 = 3
4. Complementary angles ratio
2×Board 2025Board 20263 marks
x and y are complementary angles such that x : y = 1 : 2. Express the given information as a system of linear equations in two variables and hence solve it.
5. Supplementary angles differ by 18
2×Board 2023Board 20241/3 marks
The greater of two supplementary angles exceeds the smaller by 18°. Find measures of these two angles.
Pair of Linear Equations in Two Variables questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 0 | 0 |
| Board 2023 | 4 | 6 |
| Board 2024 | 4 | 8 |
| Board 2025 | 4 | 9 |
| Sample 2025 | 2 | 4 |
| Board 2026 | 4 | 9 |
| 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 4 questions
Assertion (A) : The value of p for which the system of equations 4x + py + 8 = 0 and 2x + 2y + 2 = 0 is consistent is 4. Reason (R) : The system of equations a1x + b1y = c1 and a2x + b2y = c2 is consistent with infinitely many solutions, if a1/a2 = b1/b2 = c1/c2. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Assertion (A) is false, but Reason (R) is true.
Solve the following system of equations for x and y : x/2 + 2y/3 = – 1 and x – y/3 = 3
Solve the following system of equations graphically : x + 3y = 6; 2x – 3y = 12
x and y are complementary angles such that x : y = 1 : 2. Express the given information as a system of linear equations in two variables and hence solve it.
Sample 2026 3 questions
If 2024x + 2025y = 1 ; 2025x + 2024y = −1, then x − y =
A) 0
B) −2
C) 2
D) −1
On a particular day, 50000 people attended a Cricket Test Match between India and Australia in Sydney Cricket Ground. Let x be the number of adults attended the cricket match and y be the number of children attended the cricket match. Cost of an adult ticket was ₹1000 while cost of a child ticket was ₹200. On that day Revenue earned by selling all 50,000 tickets, was ₹4,20,00,000. Find how many adults and how many children attended the cricket match?
Solve for x and y, graphically: 2x + y = 6 ; x + y = 5
Board 2025 4 questions
Assertion (A) : The value of p for which the system of equations 4x + py + 8 = 0 and 2x + 2y + 2 = 0 is consistent is 4. Reason (R) : The system of equations a1x + b1y = c1 and a2x + b2y = c2 is consistent with infinitely many solutions, if a1/a2 = b1/b2 = c1/c2. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Assertion (A) is false, but Reason (R) is true.
Solve the following system of equations for x and y : x/2 + 2y/3 = -1 and x - y/3 = 3
Solve the following system of equations graphically : x + 3y = 6; 2x - 3y = 12
x and y are complementary angles such that x : y = 1 : 2. Express the given information as a system of linear equations in two variables and hence solve it.
Sample 2025 2 questions
The system of linear equations represented by the lines l and m is (A) consistent with unique solution (B) inconsistent (C) consistent with three solutions (D) consistent with many solutions
The sum of a two-digit number and the number obtained by reversing the order of its digits is 99. If ten's digit is 3 more than the unit's digit, then find the number.
Board 2024 4 questions
The value of k for which the pair of linear equations 5x + 2y - 7 = 0 and 2x + ky + 1 = 0 don't have a solution, is : (a) 5 (b) 4/5 (c) 5/4 (d) 5/2
Solve the following pair of linear equations for x and y algebraically: x + 2y = 9 and y - 2x = 2.
Check whether the point (-4, 3) lies on both the lines represented by the linear equations x + y + 1 = 0 and x - y = 1.
The greater of two supplementary angles exceeds the smaller by 18°. Find measures of these two angles.
Board 2023 4 questions
The larger of two supplementary angles exceeds the smaller by 18 degrees. What is the measure of larger angle ? (a) 81° (b) 99° (c) 36° (d) 54°
Assertion (A) : The system of linear equations 3x + 5y − 4 = 0 and 15x + 25y − 25 = 0 is inconsistent. Reason (R) : The pair of linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 is inconsistent if a1/a2 = b1/b2 ≠ c1/c2. (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A). (c) Assertion (A) is true, but Reason (R) is false. (d) Assertion (A) is false, but Reason (R) is true.
Solve for x and y : x + y = 6, 2x − 3y = 4.
Find out whether the following pair of linear equations are consistent or inconsistent : 5x − 3y = 11, −10x + 6y = 22.
Frequently asked questions
What are the most important topics in CBSE Class 10 Mathematics (Basic) Chapter 3 Pair of Linear Equations in Two Variables?
By how often and how recently they were asked: Word problems on pair of linear equations; Graphical solution of a pair of linear equations; Solving by elimination method.
How many marks does Pair of Linear Equations in Two Variables carry in the CBSE Class 10 Mathematics (Basic) 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 3.0 questions per paper.
Do questions from Pair of Linear Equations in Two Variables repeat in board exams?
Yes — 5 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.