Which of the following pairs is inconsistent?
Answer and explanation
Correct answer: x + 4y = 6 and 2x + 8y = 13
In option A, \(a_1/a_2=1/2\) and \(b_1/b_2=4/8=1/2\), but \(c_1/c_2=6/13\). Thus, \(a_1/a_2=b_1/b_2\ne c_1/c_2\), so the two lines are distinct and parallel and the pair has no solution. Hence, it is inconsistent. In option C, all three ratios are equal, so the pair is dependent and consistent. Exam tip: For an inconsistent pair, check whether \(a_1/a_2=b_1/b_2\ne c_1/c_2\).
Frequently asked questions
What is the correct answer to this question?
x + 4y = 6 and 2x + 8y = 13
Why is this the correct answer?
In option A, \(a_1/a_2=1/2\) and \(b_1/b_2=4/8=1/2\), but \(c_1/c_2=6/13\). Thus, \(a_1/a_2=b_1/b_2\ne c_1/c_2\), so the two lines are distinct and parallel and the pair has no solution. Hence, it is inconsistent. In option C, all three ratios are equal, so the pair is dependent and consistent. Exam tip: For an inconsistent pair, check whether \(a_1/a_2=b_1/b_2\ne c_1/c_2\).
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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