MCQs on Chapter 3 'Pair of Linear Equations in Two Variables' for Class 10 Maths

MCQs on Chapter 3: Pair of Linear Equations in Two Variables for Class 10 are available in this Maths article along with a free PDF for offline practice. These multiple‑choice questions help students practise the key concepts from Chapter 3 of the CBSE Maths syllabus in an exam‑oriented format. The MCQs with answers and detailed solutions, prepared by our subject experts, cover graphical and algebraic methods of solving linear equations (substitution, elimination, cross‑multiplication), conditions for consistency, equations reducible to linear form, and word problems involving real‑life situations to strengthen conceptual understanding and improve problem‑solving skills. By practising MCQs on Chapter 3: Pair of Linear Equations in Two Variables, students can improve accuracy, understand formulas better, and build confidence for board exams.

MCQS on Chapter 3: Pair of Linear Equations in Two Variables for Class 10 With Answers

Question 1: The pair of equations x + 2y – 5 = 0 and –4x – 8y + 20 = 0 has:

(A) A unique solution

(B) Exactly two solutions

(C) Infinitely many solutions

(D) No solution

Answer: (C) Infinitely many solutions

Explanation: a₁/a₂ = 1/(–4), b₁/b₂ = 2/(–8) = 1/(–4), c₁/c₂ = –5/20 = –1/4.

Since a₁/a₂ = b₁/b₂ = c₁/c₂, the lines are coincident and there are infinitely many solutions.

Question 2: The pair of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 has:

(A) Unique solution

(B) Exactly two solutions

(C) Infinitely many solutions

(D) No solution

Answer: (D) No solution

Explanation: a₁/a₂ = 9/18 = 1/2; b₁/b₂ = 3/6 = 1/2; c₁/c₂ = 12/26 = 6/13.

Since a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the lines are parallel to each other and never intersect; there is no solution.

Question 3: The pair of equations 5x – 15y = 8 and 3x – 9y = 24/5 has:

(A) One solution

(B) Two solutions

(C) Infinitely many solutions

(D) No solution

Answer: (C) Infinitely many solutions

Explanation: a₁/a₂ = 5/3; b₁/b₂ = –15/(–9) = 5/3; c₁/c₂ = –8/(–24/5) = –8 × (–5/24) = 40/24 = 5/3. All three ratios are equal (5/3), so the pair has infinitely many solutions.

Question 4: If the lines 3x + 2ky – 2 = 0 and 2x + 5y + 1 = 0 are parallel, what is the value of k?

(A) 4/15

(B) 15/4

(C) 4/5

(D) 5/4

Answer: (B) 15/4

Explanation: For parallel lines, a₁/a₂ = b₁/b₂ ≠ c₁/c₂. So 3/2 = 2k/5. Cross-multiplying: 15 = 4k ⇒ k = 15/4.

Question 5: If one equation of a pair of dependent linear equations is –3x + 5y – 2 = 0, a possible second equation is:

(A) –6x + 10y – 4 = 0

(B) 6x – 10y – 4 = 0

(C) 6x + 10y – 4 = 0

(D) –6x + 10y + 4 = 0

Answer: (A) –6x + 10y – 4 = 0

Explanation: Dependent equations have a₁/a₂ = b₁/b₂ = c₁/c₂. For option (A): (–3)/(–6) = 5/10 = (–2)/(–4) = 1/2. All three ratios are equal, confirming dependence.

Question 6: If the graphical representation of a pair of linear equations is two parallel lines, the pair is:

(A) Consistent with a unique solution

(B) Consistent with infinitely many solutions

(C) Inconsistent

(D) Dependent

Answer: (C) Inconsistent

Explanation: Parallel lines never meet, so there is no point of intersection and hence no solution. A system with no solution is called inconsistent.

Question 7: The graphical representation of the pair of equations 4x + 3y – 6 = 5 and 12x + 9y = 15 will be:

(A) Parallel lines

(B) Coincident lines

(C) Intersecting lines

(D) Perpendicular lines

Answer: (A) Parallel lines

Explanation: Rewrite: 4x + 3y = 11 and 12x + 9y = 15.

a₁/a₂ = 4/12 = 1/3; b₁/b₂ = 3/9 = 1/3; c₁/c₂ = 11/15.

Since a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the lines are parallel.

Question 8: The solution of the equations x – y = 2 and x + y = 4 is:

(A) x = 3, y = 1

(B) x = 4, y = 3

(C) x = 5, y = 1

(D) x = –1, y = –3

Answer: (A) x = 3, y = 1

Explanation: Adding the two equations: 2x = 6, so x = 3. Substituting back: 3 – y = 2, so y = 1.

Question 9: The solution of the pair of equations 2x + y = 5 and 3x + 2y = 8 is:

(A) x = 1, y = 2

(B) x = 2, y = 1

(C) x = –1, y = 7

(D) x = 3, y = –1

Answer: (B) x = 2, y = 1

Explanation: From equation 1: y = 5 – 2x. Substituting into equation 2: 3x + 2(5 – 2x) = 8 ⇒ 3x + 10 – 4x = 8 ⇒ –x = –2 ⇒ x = 2. Then y = 5 – 4 = 1.

Question 10: A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. The fraction is:

(A) 3/12

(B) 4/12

(C) 5/12

(D) 7/12

Answer: (C) 5/12

Explanation: Let the fraction be x/y.

Condition 1: (x – 1)/y = 1/3 ⇒ 3x – y = 3 … (i)

Condition 2: x/(y + 8) = 1/4 ⇒ 4x – y = 8 … (ii)

Subtracting (i) from (ii): x = 5. From (ii): y = 12. Fraction = 5/12.

Question 11: The father's age is six times his son's age. Four years hence, the father will be four times his son's age. Their present ages (son, father) are:

(A) 4 years and 24 years

(B) 5 years and 30 years

(C) 6 years and 36 years

(D) 3 years and 24 years

Answer: (C) 6 years and 36 years

Explanation: Let son's age = y and father's age = x.

Equation 1: x = 6y

Equation 2: x + 4 = 4(y + 4) ⇒ x – 4y = 12

Substituting (1) into (2): 6y – 4y = 12 ⇒ y = 6, x = 36.

Question 12: Ritu can row downstream 20 km in 2 hours and upstream 4 km in 2 hours. Her speed in still water and the speed of the current are respectively:

(A) 6 km/h and 3 km/h

(B) 7 km/h and 4 km/h

(C) 6 km/h and 4 km/h

(D) 10 km/h and 6 km/h

Answer: (C) 6 km/h and 4 km/h

Explanation: Let Ritu's speed in still water = x km/h and speed of stream = y km/h.

Downstream speed = x + y; upstream speed = x – y.

2(x + y) = 20 ⇒ x + y = 10 … (i)

2(x – y) = 4 ⇒ x – y = 2 … (ii)

Adding: 2x = 12 ⇒ x = 6. From (i): y = 4.

Question 13: If 2/(x+y) + 3/(x–y) = 2 and 4/(x+y) – 9/(x–y) = –1, which substitution simplifies the system?

(A) Let p = x + y and q = x – y

(B) Let p = 1/(x+y) and q = 1/(x–y)

(C) Let p = 1/x and q = 1/y

(D) Let p = x – y and q = x + y

Answer: (B) Let p = 1/(x+y) and q = 1/(x–y)

Explanation: Substituting p = 1/(x+y) and q = 1/(x–y) converts the equations to 2p + 3q = 2 and 4p – 9q = –1, which are standard linear equations.

Question 14: For the equations 2x + 3y = 7 and 2ax + (a + b)y = 28 to have infinitely many solutions:

(A) a = 2b

(B) b = 2a

(C) a + 2b = 0

(D) 2a + b = 0

Answer: (B) b = 2a

Explanation: For infinitely many solutions: 2/(2a) = 3/(a+b) = 7/28.

From 7/28 = 1/4 and 2/(2a) = 1/4 ⇒ a = 4.

From 3/(a+b) = 1/4 ⇒ a + b = 12 ⇒ b = 8.

Check: b = 2a ⇒ 8 = 2(4)

Question 15: Aruna has only ₹1 and ₹2 coins in her purse. If the total number of coins is 50 and the total amount is ₹75, the number of ₹1 and ₹2 coins are respectively:

(A) 35 and 15

(B) 15 and 35

(C) 25 and 25

(D) 20 and 30

Answer: (C) 25 and 25

Explanation: Let x = number of ₹1 coins and y = number of ₹2 coins.

x + y = 50 … (i)

x + 2y = 75 … (ii)

Subtracting: y = 25. Then x = 25.

 

Click here to download the free PDF of MCQs worksheet on Chapter 3: Pair of Linear Equations in Two Variables for Class 10 Maths based on the updated NCERT & CBSE pattern with important multiple-choice questions and answers.

MCQs Worksheet on Chapter 3: Pair of Linear Equations in Two Variables for Class 10