CBSE Class 10 Maths Chapter 3: Pair of Linear Equations in Two Variables is a high-weightage chapter that helps students build strong algebraic and graphical problem-solving skills. This chapter introduces the concept of two linear equations taken together, explains how their solutions represent the point(s) of intersection of two lines, and covers important solving techniques like the substitution method, elimination method, and cross-multiplication method. Students also learn conditions for unique solutions, no solution, and infinitely many solutions, which are frequently asked in CBSE board exams.
This chapter forms the base for advanced mathematics topics and competitive exams, making it essential for students to practice NCERT questions, previous year papers, case-study questions, and HOTS questions. A clear understanding of Chapter 3 not only boosts board exam scores but also strengthens logical reasoning and real-life application skills. Check the article in details to get the important questions for CBSE Class 10 Maths Chapter 3 with answers and a free PDF to download.
CBSE Class 10 Maths Exam 2026: Key Highlights
| Particulars | Details |
| Board | Central Board of Secondary Examination (CBSE) |
| Exam Mode | Offline |
| Subject | Mathematics |
| Paper Name | Maths Standard and Maths Basic |
| Chapter Weightage | 6 Marks (Standard) 9 Marks (Basic) |
| Medium/ Language | English and Hindi |
| Exam Duration | 3 Hours |
| Total Marks | 100 |
| Theory Paper | 80 Marks |
| Internal Assessment | 20 Marks |
| Also Check: CBSE Class 10 Maths Chapter 1 Real Numbers Important Questions with Answers |
Important Questions and Answers for CBSE Class 10 Maths Chapter 3: Pair of Linear Equations in Two Variables
To Check all the detailed answers of the important question of CBSE Class 10 Maths Chapter 3: Pair of Linear Equations in Two Variables, Download PDF from the link provided below:
SECTION A: ONE MARKS
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If the lines represented by 2x + ky = 7 and 6x + 5y = 11 are parallel, find the value of k.
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The pair of equations 5x - 8y + 1 = 0 and 3x - 24/5y + ⅗ = 0 has how many solutions?
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If the pair of equations x + 2y - 5 = 0 and 3x + 6y + k = 0 is inconsistent, write a possible value of k.
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If x = 3 and y = -1 is the solution of the equation ax - 5y = 14, find the value of a.
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Solve for x: x + y = 10 and x - y = 4.
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The lines x = a and y = b are considered a consistent pair. What kind of lines do they represent?
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Does the system of linear equations 2x + 3y = 8 and 4x + 6y = 16 have a finite number of solutions?
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If the difference between two numbers is 5 and the sum of the numbers is 17, find the smaller number.
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A student writes a two-digit number. The sum of its digits is 9. If the unit's digit is y and the ten's digit is x, write the linear equation representing this statement.
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State whether the following statement is True or False: Every solution of the linear equation in two variables is a point on the line representing it.
SECTION B: TWO MARKS
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For what value of k will the system of linear equations kx + 3y = k - 3 and 12x + ky = k have infinitely many solutions?
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Find the value of m for which the pair of linear equations 2x + 3y - 7 = 0 and (m-1)x + (m+1)y = 3m - 1 has no solution.
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Solve the following pair of linear equations by the substitution method:
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x + 2y = 3
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4x + 3y = 2
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Solve for x and y:
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0.4x + 0.3y = 1.7
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0.7x - 0.2y = 0.8
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Two angles are complementary. If the larger angle is 10° more than the smaller angle, find the measure of the smaller angle.
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The cost of two tables and three chairs is ₹1200. Write the linear equation representing this statement. If the cost of a table is ₹300, find the cost of one chair.
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Solve the following pair of linear equations by the substitution and cross-multiplication methods:
8x + 5y = 9
3x + 2y = 4 -
Find the value(s) of k so that the pair of equations x + 2y = 5 and 3x + ky + 15 = 0 has a unique solution.
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Check graphically whether the pair of equations 3x – 2y + 2 = 0 and 3/2x – y + 3 = 0, is consistent. Also find the coordinates of the points where the graphs of the equations meet the Y-axis.
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Represent the following pair of equations graphically and write the coordinates of points where the lines intersect the y-axis.
SECTION C: THREE MARKS
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Solve the following pair of linear equations for x and y:
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141x + 93y = 189;
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93x + 141y = 45
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Determine graphically the coordinates of vertices of a triangle, the equation of whose sides are given by 2y – x = 8, 5y – x = 14 and y – 2x = 1.
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Use elimination method to find all possible solutions of the following pair of linear equation:
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2x + 3y = 8
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4x + 6y = 7
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Solve the following pairs of equations by reducing them to a pair of linear equations:
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1/2x + 1/3y = 2
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1/3x + 1/2y = 13/6
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A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. Find the speed of the train.
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Solve for x and y:
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27x + 31y = 85;
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31x + 2 7y = 89
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The sum of the digits of a two digit number is 8 and the difference between the number and that formed by reversing the digits is 18. Find the number.
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A man earns ₹600 per month more than his wife. One-tenth of the man’s salary and l/6th of the wife’s salary amount to ₹1,500, which is saved every month. Find their incomes.
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Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu now?
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The sum of the numerator and the denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the original fraction.
SECTION D: FOUR MARKS
Case Study 1: Sita Devi wants to make a rectangular pond on the road side for the purpose of providing drinking water for street animals. The area of the pond will be decreased by 3 square feet if its length is decreased by 2 ft. and breadth is increased by 1 ft. Its area will be increased by 4 square feet if the length is increased by 1 ft. and breadth remains the same. Find the dimensions of the pond.
Case Study 2: The owner of a taxi company decides to run all the taxis on CNG fuel instead of petrol/diesel. The taxi charges in the city are fixed charges together with the charge for the distance covered. For a journey of 12 km, the charge paid is 789 and for a journey of 20 km, the charge paid is ₹145. What will a person have to pay for travelling a distance of 30 km?
Case Study 3: A man travels 300 km partly by train and partly by car. It takes 4 hours if he travels 60 km by train and the rest by car. If he travels 100 km by train and the remaining by car, he takes 10 minutes longer. Find the speeds of the train and the car separately.
Case Study 4: Amit bought two pencils and three chocolates for ₹11 and Sumeet bought one pencil and two chocolates for ₹7. Represent this situation in the form of a pair of linear equations. Find the price of one pencil and that of one chocolate graphically.
Case Study 5: The monthly charges in a hostel are fixed and the remaining depend on the number of days one has taken food in the mess. When a student A takes food for 20 days, she has to pay ₹1000 as hostel charges, whereas a student B, who takes food for 26 days, pays ₹1180.
| Also Check: CBSE Class 10 Maths Chapter 2: Polynomials Important Questions with Answers CBSE Class 10 Maths Chapter 5: Arithmetic Progressions Important Questions with Answers |
SECTION A
| Sl. No. | Answers |
| 1. | k=5/3 |
| 2. | Infinitely many solutions (Coincident lines) |
| 3. | Any value of k except k = -15. (e.g., k=1, k=10, etc.) |
| 4. | a = 3 (Since 3a - 5(-1) = 14 ⟹ 3a + 5 = 14 ⟹ 3a = 9 ⟹ a = 3$). |
| 5. | x=7 (and y=3) |
| 6. | Intersecting lines (They intersect at the unique point (a, b)). |
| 7. | No. (It has infinitely many solutions) |
| 8. | The smaller number is 6. (x=11, y=6) |
| 9. | x + y = 9 |
| 10. | True |
SECTION B
| Sl.No. | Answers |
| 1. | k=6 |
| 2. |
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| 3. | x = -1, y = 2. |
| 4. | x = 2, y = 3. |
| 5. | The smaller angle (y) is 40° |
| 6. | The equation is 2x + 3y = 1200. The cost of one chair (y) is ₹200. |
| 7. |
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| 8. |
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| 9. |
By plotting the points and joining them, the lines do not intersect anywhere, i.e., they are parallel. Therefore a given pair of equations is not consistent, i.e., inconsistent. The equation 3x – 2y + 2 = 0 meets the Y-axis at A(0,1). The equation 3/2x – y + 3 = 0 meets the Y-axis at B(0, 3). |
| 10. |
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SECTION C
| Sl.No. | Answers | ||||||||||||||||||||||||
| 1. |
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| 2. | Given, 2y – x = 8….(i) 5y – x = 14….(ii) y – 2x = 1….(iii) From (i), 2y = x + 8 y = (x + 8)/2
From (ii), 5y = x + 14 y = (x + 14)/5
From (iii), y = 2x + 1
Let us plot all these points on the graph.From the graph, we can write the coordinates of vertices of triangle formed are: P(-4, 2), Q(1, 3), and R(2, 5) | ||||||||||||||||||||||||
| 3. | Given, 2x + 3y = 8….(i) 4x + 6y = 7….(ii) Multiply Equation (1) by 2 and Equation (2) by 1 to make the coefficients of x equal. 4x + 6y = 16….(iii) 4x + 6y = 7….(iv) Subtracting (iv) from (iii), 4x + 6y – 4x – 6y = 16 – 7 0 = 9, it is not possible Therefore, the pair of equations has no solution. | ||||||||||||||||||||||||
| 4. | Given, 1/2x + 1/3y = 2 1/3x + 1/2y = 13/6 Let us assume 1/x = m and 1/y = n , then the equations will change as follows. m/2 + n/3 = 2 ⇒ 3m+2n-12 = 0….(1) m/3 + n/2 = 13/6 ⇒ 2m+3n-13 = 0….(2) Now, using cross-multiplication method, we get, m/(-26-(-36) ) = n/(-24-(-39)) = 1/(9-4) m/10 = n/15 = 1/5 m/10 = 1/5 and n/15 = 1/5 So, m = 2 and n = 3 1/x = 2 and 1/y = 3 x = 1/2 and y = 1/3 | ||||||||||||||||||||||||
| 5. | The uniform speed of the train is 40km/h. | ||||||||||||||||||||||||
| 6. |
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| 7. | Let unit and tens digit be x and y. ∴ Original number = 1x + 10y …(i) Reversed number = 10x + 1y According to question, x + y = 8 ⇒ y = 8 – x …(ii) Also, 1x + 10Oy – (10x + y) = 18 ⇒ x + 10y – 10x – y = 18 ⇒ 9y – 9x = 18 ⇒ y – x = 2 …[Dividing both sides by 9 ⇒ 8 – x – x = 2 …[From (it) ⇒ 8 – 2 = 2x ⇒ 2x = 6 From (it), y = 8 – 3 = 5 From (i), Original number = 3 + 10(5) = 53 | ||||||||||||||||||||||||
| 8. | Wife’s income = ₹x = ₹5,400 Man’s income = ₹(x + 600) = ₹6,000 | ||||||||||||||||||||||||
| 9. | Nuri's age is 50 years and Sonu's age is 20 years. | ||||||||||||||||||||||||
| 10. | The original fraction is 5/7 |
SECTION D
| Sl.No. | Answers |
| 1. | Let length of rectangular pond = x and breadth of rectangular pond = y Area of rectangular pond = xy According to Question,
∴Length of rectangular pond = 7 ft. Breadth of rectangular pond = 4 ft. |
| 2. | Total fare for 30 km = x + 30y = 5 + 30(7) = 5 + 210 = ₹215 |
| 3. | Speed of the train = 60 km/hr and Speed of the car = 80 km/hr |
| 4. | Lines intersect at (1, 3). ∴ x = 1, y = 3 Therefore the price of one pencil = ₹1 and price of one chocolate = ₹3 |
| 5. |
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CBSE Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables: Download PDF of Important Questions and Answers |
Practicing these CBSE Class 10 Maths Chapter 3 (Pair of Linear Equations in Two Variables) important questions helps students master essential algebraic techniques and understand how equations represent real-life situations. With consistent practice of NCERT, previous year questions, and different solving methods, students can score high in exams. This chapter strengthens analytical thinking and forms a strong base for higher-level mathematics.
| Also Check: |
CBSE Class 10 Maths Board Exams requires focused practice on high-yield questions from all chapters. To streamline your revision and ensure you cover only the most important questions guaranteed to boost your confidence, you can instantly access the complete, chapter-wise compilation specifically designed for dedicated board students simply click the below link to get the important questions of CBSE Class 10 maths of all chapters from here for board students.
| CHECK: CBSE Class 10 Maths Important Questions with Answers 2026: All Subjects |
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