Pair of Linear Equations: Class 10 Previous Year Questions

Pair of Linear Equations questions asked in CBSE board exams

Repeated questions first. Open the free app to see each question as it appeared in the paper, with its marking scheme.

1. If a pair of linear equations in two variables is represented by two coincident lines, then the pair of equations has : (a) a unique solution (b) two solutions (c) no solution (d) an infinite number of solutions
   Board 20261 markMCQ
2. If the pair of linear equations : aix + biy + Ci = O and a2x + b2y + C2 = 0 is consistent and dependent, then (A) b2 a2 bi a1 (B) a2 b2 C2 b1 (C) a2 b2 C2 bi (D) a2 b2 C2
   Board 20261 markMCQ
3. Aarush bought 2 pencils and 3 chocolates for 11 and Tanish bought 1 pencil and 2 chocolates for 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.
   Board 20265 markslong answer
4. Assertion (A) : The pair of linear equations px + 3y + 59 = 0 and 2x + 6y + 118 = 0 will have infinitely many solutions if p = 1. Reason (R): If the pair of linear equations px + 3y + 19 = 0 and 2x + 6y + 157 = 0 has a unique solution, then p 1.
   Board 20251 markAssertion-Reason
5. 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 =
   Board 20251 markMCQ
6. | P a g e 36. A school is organizing a grand cultural event to show the talent of its students. To accommodate the guests, the school plans to rent chairs and tables from a local supplier. It finds that rent for each chair is 50 and for each table is 200. The …
   Board 20254 marksshort answer
7. In the given figure, graphs of two linear equations are shown. 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 extendin…
   Board 20241 markAssertion-Reason
8. (a) Solve the pair of equations x = 3 and y = -4 graphically. OR (b) Using graphical method, find whether following system of linear equations is consistent or not : x= 0 and y=-7
   Board 20232 marksshort answer
9. JJJJ Page 14 30. (H$) `{X a¡{IH$ g_rH$aU {ZH$m` 2x + 3y = 7 VWm 2ax + (a + b)y = 28 Ho$ An[a{_V ê$n go AZoH$ hb hm|, Vmo Am¡a Ho$ _mZ kmV H$s{OE & AWdm (I) `{X 217x + 131y = 913 Am¡a 131x + 217y = 827 hm|, Vmo x Am¡a y Ho$ _mZ kmV H$aZo Ho$ {bE g_rH$aU hb H$s{…
   Board 20233 marksshort answer
10. For the given pair of equations, two statements are given below - one labelled Assertion (A) and the other labelled Reason (R). Read the statements carefully and choose the option that correctly describes statements (A) and (R). 2 𝑥+ 5𝑦= 15 3 𝑥+ 6𝑦= 7 Assertio…
    CBSE practice 2021-221 markAssertion-Reason
11. Two statements are given below - one labelled Assertion (A) and the other labelled Reason (R). Read the statements carefully and choose the option that correctly describes statements (A) and (R). Assertion (A): 9 x + 12 y - 7 = 0 and 6 x + 8 y - 14 = 0 form a …
    CBSE practice 2021-221 markAssertion-Reason
12. Shown below is a pair of linear equations. mx + 4y - 6 = 0 ny - 12x + 12 = 0 For which of the following values of m and n do the above equations have infinitely many solutions? A) m = -1 and n = 2 B) m = -1 and n = 3 C) m = 6 and n = -8 D) m = 6 and n = -2
    CBSE practice 2022-231 markvery short
13. Given below is a pair of linear equations: 2x - my = 9 4x - ny = 9 Find at least one pair of the possible values of m and n, if exists, for which the above pair of linear equations has: i) a unique solution ii) infinitely many solutions iii) no solution Show y…
    CBSE practice 2023-243 marksshort answer
14. A student entrepreneur started a company that manufactures sanitizers in two sizes – small and large. The cost of a small bottle of sanitizer is ₹10 and that of a large bottle is ₹15. In June, the company sold 1000 bottles and recorded a total sale of ₹12,750.…
    Sample paper 2026-274 marksshort answer
15. The lines k1, k2 and k3 represent three different equations as shown in the graph below. The solution of the equations represented by the lines k1 and k3 is x = 3 and y = 0 while the solution of the equations represented by the lines k2 and k3 is x = 4 and y =…
    CBSE practice 2023-241 markMCQ
16. Tarun correctly solved a pair of linear equations in two variables and found their only point of intersection as (5, – 1). One of the lines was x – y = 6. Which of the following could have been the other line? I: 3x – 3y = 18 II: 2x – 3y = 13 III: 2x – 3y = 16…
    Sample paper 2026-271 markMCQ

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