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. (a) Find the value of c for which the following pair of linear equations has infinitely many solutions : cx + 3y = c 3 12x + cy = c OR (b) Solve for x and y : 3x + 2y = 65 2x + 3y = 60
   Board 20252 marksshort answerRepeated: 2024,2025
2. 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 1 2 a a = = .
   Board 20251 markAssertion-Reason
3. | P a g e 20. Assertion (A) : All congruent triangles are similar. Reason (R) : In congruent triangles, the ratio of corresponding sides is 1 : 1. 10| P a g e 5 - (VSA) 2 5 2=10 21. ( ) c cx + 3y = c 3 12x + cy = c ( ) x y 3x + 2y = 65 2x + 3y = 60 22. ABC BC …
   Board 20251 markAssertion-Reason
4. | P a g e 28. (a) Solve the following system of equations graphically : x + 3y = 6; 2x 3y = 12 OR (b) 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. 1…
   Board 20253 marksshort answer
5. (a) Solve graphically the following pair of linear equations : 2x y = 2 and 4x y = 4 Also, write the coordinates of the points where the lines represented by these equations cut the y-axis. OR (b) An academy offering cricket coaching bought 10 bats and 5 balls…
   Board 20253 marksshort answer
6. (A) Solve the following pair of linear equations for x and y algebraically : x + 2y = 9 and y - 2x = 2 OR (B) Check whether the point (- 4, 3) lies on both the lines represented by the linear equations x + y + 1 = O and x - y= 1.
   Board 20242 marksshort answer
7. The value of k for which the pair of linear equations 5x+2y-7=0 and 2x+ky+l = 0 don't have a solution, is : (b) (c) (a) (d) C3ABD/1 /31 Page 5 (b) (a) (c) (d) 36 36 () ) 6 (), (A) (R) (R), (A) (b) (A)(R)(R),(A) (c) (A) (R) (d) 19. h d h : ) PBOAPB (R) : 20. (A…
   Board 20241 markMCQ
8. Solve for x and y : x + y = 6, 2x - 3y = 4. (a) OR (b) Find out whether the following pair of linear equations are consistent or inconsistent : 5x- 3y = 11, -10x + 6y = 22
   Board 20232 marksshort answer
9. Assertion (A): The system of linear equations 3x + 5y - 4 = 0 and 15x+25y-25=0isinconsistent. Reason(R): The pair of linear equations ajx + biy + ci = O and a2x + b2y + C2 = 0 is inconsistent if a2 C2
   Board 20231 markAssertion-Reason
10. The pair of linear equations x + 2y 5 = 0 and 2x 4y + 6 = 0 : (a) is inconsistent (b) is consistent with many solutions (c) is consistent with a unique solution (d) is consistent with two solutions
    Board 20231 markMCQ
11. The lines represented by the linear equations y = x and x = 4 intersect at P. The coordinates of the point P are : (a) (4, 0) (b) (4, 4) (c) (0, 4) (d) ( 4, 4)
    Board 20231 markMCQ

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