Chapter Exam

Chapter 4: Pair of Linear Equations in Two Variables — Online MCQ Test

Q: A pair of linear equations is said to be consistent if it has:

Answer: B. At least one solution — Consistent pair of linear equations have at least one solution, which can be unique or infinite. Inconsistent pairs have no solution.

Q: Two lines represented by the equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 are parallel if:

Answer: A. a₁/a₂ = b₁/b₂ ≠ c₁/c₂ — Parallel lines have equal slopes but different intercepts, represented by the ratio condition a₁/a₂ = b₁/b₂ ≠ c₁/c₂.

Q: If the pair of linear equations 3x + 4y = 12 and 9x + 12y = k has infinitely many solutions, then k =

Answer: B. 36 — For infinitely many solutions, a₁/a₂ = b₁/b₂ = c₁/c₂. Here, 3/9 = 4/12 = 12/k, so 1/3 = 12/k, giving k = 36.

Q: The condition for a pair of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 to have a unique solution is:

Answer: B. a₁b₂ - a₂b₁ ≠ 0 — A unique solution exists when a₁b₂ - a₂b₁ ≠ 0, which means the lines are not parallel and not coincident.

MATHS · CLASS 10th · Telangana State Board

Practice Chapter 4: Pair of Linear Equations in Two Variables with a free chapter-wise online MCQ test for Telangana State Board CLASS 10th MATHS. This chapter covers: This chapter focuses on systems of two linear equations. Students learn to determine consistency. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter 4: Pair of Linear Equations in Two Variables — Important Questions & Answers (FAQ)

Frequently asked questions from Telangana State Board CLASS 10th MATHS — Chapter 4: Pair of Linear Equations in Two Variables, with answers and explanations. These are sample questions; the exam has its own separate question set.

A pair of linear equations is said to be consistent if it has:

A. No solution
B. At least one solution ✓
C. Exactly two solutions
D. Infinitely many solutions only

Answer: B. At least one solution
Consistent pair of linear equations have at least one solution, which can be unique or infinite. Inconsistent pairs have no solution.

Two lines represented by the equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 are parallel if:

A. a₁/a₂ = b₁/b₂ ≠ c₁/c₂ ✓
B. a₁/a₂ ≠ b₁/b₂
C. a₁/a₂ = b₁/b₂ = c₁/c₂
D. a₁b₂ = a₂b₁

Answer: A. a₁/a₂ = b₁/b₂ ≠ c₁/c₂
Parallel lines have equal slopes but different intercepts, represented by the ratio condition a₁/a₂ = b₁/b₂ ≠ c₁/c₂.

If the pair of linear equations 3x + 4y = 12 and 9x + 12y = k has infinitely many solutions, then k =

A. 24
B. 36 ✓
C. 48
D. 60

Answer: B. 36
For infinitely many solutions, a₁/a₂ = b₁/b₂ = c₁/c₂. Here, 3/9 = 4/12 = 12/k, so 1/3 = 12/k, giving k = 36.

The condition for a pair of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 to have a unique solution is:

A. a₁b₂ - a₂b₁ = 0
B. a₁b₂ - a₂b₁ ≠ 0 ✓
C. a₁/a₂ = b₁/b₂
D. a₁ = a₂ and b₁ = b₂

Answer: B. a₁b₂ - a₂b₁ ≠ 0
A unique solution exists when a₁b₂ - a₂b₁ ≠ 0, which means the lines are not parallel and not coincident.

The system of equations 2x + 3y = 6 and 4x + 6y = 12 and the system 2x + 3y = 7 and 4x + 6y = 14 differ in that the first is _______ while the second is _______:

A. Inconsistent; inconsistent
B. Consistent with infinite solutions; consistent with infinite solutions
C. Consistent with infinite solutions; inconsistent ✓
D. Inconsistent; consistent with unique solution

Answer: C. Consistent with infinite solutions; inconsistent
First system: 4x + 6y = 12 is 2×(2x + 3y = 6), so coincident/infinite solutions. Second system: 4x + 6y = 14 ≠ 2×7, lines are parallel/no solution (inconsistent).

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