Chapter 4: Pair of Linear Equations in Two Variables — Online MCQ Test
MATHS · CLASS 10th · Telangana State Board
Practice Chapter 4: Pair of Linear Equations in Two Variables with a free chapter-wise online MCQ test.
This chapter covers: This chapter focuses on systems of two linear equations. Students learn to determine consistency.
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Chapter 4: Pair of Linear Equations in Two Variables — Important Questions & Answers
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.
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.
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.
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.
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).
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).