What kind of pair is (13x+5y=22) and (26x+10y=45)?
Answer and explanation
Correct answer: Inconsistent (parallel and distinct lines)
For the two equations, 13/26 = 5/10 = 1/2, but 22/45 is not equal to 1/2. Thus, a₁/a₂ = b₁/b₂, while c₁/c₂ is different. Therefore, the two lines are parallel and distinct, so they have no common solution and the pair is inconsistent. Exam tip: When a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the pair is inconsistent.
Frequently asked questions
What is the correct answer to this question?
Inconsistent (parallel and distinct lines)
Why is this the correct answer?
For the two equations, 13/26 = 5/10 = 1/2, but 22/45 is not equal to 1/2. Thus, a₁/a₂ = b₁/b₂, while c₁/c₂ is different. Therefore, the two lines are parallel and distinct, so they have no common solution and the pair is inconsistent. Exam tip: When a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the pair is inconsistent.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Conditions for solvability.
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