What type of pair is (12x+18y=42) and (2x+3y=8)?
Answer and explanation
Correct answer: Inconsistent
For the two equations, \(a_1/a_2=12/2=6\) and \(b_1/b_2=18/3=6\), but \(c_1/c_2=42/8=21/4\). Thus, \(a_1/a_2=b_1/b_2\neq c_1/c_2\), so the two lines are distinct and parallel. Hence, the pair has no solution and is inconsistent. A coincident or dependent pair requires all three ratios to be equal. Exam tip: compare \(a_1/a_2\), \(b_1/b_2\), and \(c_1/c_2\) systematically.
Frequently asked questions
What is the correct answer to this question?
Inconsistent
Why is this the correct answer?
For the two equations, \(a_1/a_2=12/2=6\) and \(b_1/b_2=18/3=6\), but \(c_1/c_2=42/8=21/4\). Thus, \(a_1/a_2=b_1/b_2\neq c_1/c_2\), so the two lines are distinct and parallel. Hence, the pair has no solution and is inconsistent. A coincident or dependent pair requires all three ratios to be equal. Exam tip: compare \(a_1/a_2\), \(b_1/b_2\), and \(c_1/c_2\) systematically.
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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