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Class 10 Pair of Linear Equations: 8 practice questions with answers, step by step
These are 8 practice questions on NCERT Class 10 Maths Chapter 3, Pair of Linear Equations in Two Variables, each with a worked answer. They cover the three things the chapter asks: solving a pair by substitution or elimination, saying how many solutions a pair has, and turning a word problem into two equations. Try each one on paper before you open the answer.
These questions are our own, drafted with AI help. Every answer was re-computed by a test script, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.
What the chapter says you need
Five facts from the NCERT textbook (Mathematics, Textbook for Class X, Reprint 2026-27, Chapter 3, printed pages 24 to 37) cover every question below:
- A pair of linear equations that has a solution is consistent; a pair with no solution is inconsistent (section 3.2, page 25).
- Graphically, the two equations are two lines. If the lines intersect at a point, that point is the unique solution. If the lines coincide, there are infinitely many solutions (the pair is dependent and consistent). If the lines are parallel, there is no solution (summary, section 3.4, page 37).
- Substitution method: write one variable in terms of the other from one equation, and put it into the other equation (section 3.3.1, page 30).
- Elimination method: make the coefficients of one variable equal and add or subtract the equations so that variable disappears (section 3.3.2, page 34).
- For a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0: if a1/a2 ≠ b1/b2 the pair is consistent (one solution); if a1/a2 = b1/b2 ≠ c1/c2 it is inconsistent; if a1/a2 = b1/b2 = c1/c2 it is dependent and consistent (summary, page 37).
Solving a pair
Question 1. Solve x + 2y = 11 and x − y = 2. What is y?
Answer: Subtract the second equation from the first: (x + 2y) − (x − y) = 11 − 2, so 3y = 9 and y = 3. Then x = 2 + y = 5. Check: 5 + 6 = 11 and 5 − 3 = 2.
Question 2. Solve 2x + 3y = 13 and x − y = −1. What is x?
Answer: From the second equation, x = y − 1. Put it into the first: 2(y − 1) + 3y = 13, so 5y = 15, y = 3 and x = 2. Check: 4 + 9 = 13 and 2 − 3 = −1.
How many solutions?
Question 3. How many solutions do 2x + 3y = 6 and 4x + 6y = 12 have?
Answer: Here a1/a2 = 2/4 = 1/2, b1/b2 = 3/6 = 1/2 and c1/c2 = 6/12 = 1/2. All three ratios are equal, so the lines coincide: the pair is dependent and consistent, with infinitely many solutions. (Indeed the second equation is just twice the first.)
Question 4. For what values of k do kx + 2y = 5 and 3x + y = 1 have exactly one solution?
Answer: A unique solution needs a1/a2 ≠ b1/b2, that is k/3 ≠ 2/1, so k ≠ 6. The pair has exactly one solution for every k except k = 6. Check the exception: when k = 6 the equations are 6x + 2y = 5 and 6x + 2y = 2, which cannot both be true, so the lines are parallel and there is no solution.
Word problems
For a word problem: let the two unknown quantities be x and y, write the two facts the question gives as two equations, solve them, and check the answer against the story.
Question 5. The sum of two numbers is 50 and their difference is 14. Find the larger number.
Answer: Let the numbers be x and y with x larger: x + y = 50 and x − y = 14. Adding gives 2x = 64, so x = 32 (and y = 18). Check: 32 + 18 = 50 and 32 − 18 = 14.
Question 6. 5 pencils and 2 pens cost ₹60. 3 pencils and 2 pens cost ₹48. What does one pencil cost, in rupees?
Answer: Subtract the second from the first: 2 pencils cost 60 − 48 = ₹12, so one pencil costs ₹6. (Then 5 × 6 + 2 × pen = 60 gives a pen at ₹15; check 3 × 6 + 2 × 15 = 48.)
Question 7. A father is 3 times as old as his son. In 10 years he will be twice as old as the son. How old is the son now?
Answer: Let the son be s years old; the father is 3s. In 10 years: 3s + 10 = 2(s + 10), so 3s + 10 = 2s + 20 and s = 10. The son is 10 and the father 30; in 10 years they will be 20 and 40.
Question 8. 5 notebooks and 7 pens cost ₹50, while 7 notebooks and 5 pens cost ₹46. What does one pen cost, in rupees?
Answer: Let a notebook cost x and a pen y: 5x + 7y = 50 and 7x + 5y = 46. Adding gives 12x + 12y = 96, so x + y = 8. Subtracting the second from the first gives 2y − 2x = 4, so y − x = 2. Then y = 5: one pen costs ₹5 (and a notebook ₹3). Check: 15 + 35 = 50 and 21 + 25 = 46.
Practise more, and check your marks
- Free practice, marked instantly in your browser: Class 10 Pair of Linear Equations questions. Questions 1, 2, 5, 6, 7 and 8 above are in this set.
- Printable worksheets with answer keys, in English, Hindi and Marathi: Class 10 worksheets.
- See which unit this chapter belongs to and how CBSE splits the 80 theory marks in our Class 10 Maths syllabus 2026-27 guide.
- The same step-by-step style for the next chapters: Class 10 Quadratic Equations and Class 10 Arithmetic Progressions.
Where CMDLearn fits
CMDLearn is building an AI tutor for Classes 1 to 10 that explains a step and checks the child's working, but leaves the writing to the child. It is still in development, and no child uses it yet. If you would like to hear when there is something to try, you can join the waitlist.
Sources
All opened and read on 21 October 2026. Page numbers are the printed page numbers of the textbook.
- NCERT, Mathematics, Textbook for Class X, Chapter 3 "Pair of Linear Equations in Two Variables" (Reprint 2026-27), printed pages 24-37 (consistent and inconsistent pairs, section 3.2, page 25; the substitution method, section 3.3.1, page 30; the elimination method, section 3.3.2, page 34; the graphical outcomes and the a1/a2, b1/b2, c1/c2 conditions, summary, section 3.4, page 37): ncert.nic.in/textbook/pdf/jemh103.pdf
The definitions and conditions are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the official CBSE notices.