What kind of pair is (4x+y-3=0) and (8x+2y-5=0)?
Answer and explanation
Correct answer: A pair with no solution
Here, \(a_1/a_2=4/8=1/2\), \(b_1/b_2=1/2\), but \(c_1/c_2=(-3)/(-5)=3/5\). Thus, \(a_1/a_2=b_1/b_2\ne c_1/c_2\), so the two lines are distinct and parallel. Therefore, the pair has no solution and is inconsistent. Option C is incorrect because infinitely many solutions require all three ratios to be equal. Exam tip: if \(a_1/a_2=b_1/b_2\ne c_1/c_2\), the pair is inconsistent.
Frequently asked questions
What is the correct answer to this question?
A pair with no solution
Why is this the correct answer?
Here, \(a_1/a_2=4/8=1/2\), \(b_1/b_2=1/2\), but \(c_1/c_2=(-3)/(-5)=3/5\). Thus, \(a_1/a_2=b_1/b_2\ne c_1/c_2\), so the two lines are distinct and parallel. Therefore, the pair has no solution and is inconsistent. Option C is incorrect because infinitely many solutions require all three ratios to be equal. Exam tip: if \(a_1/a_2=b_1/b_2\ne c_1/c_2\), 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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