Which option is correct for (6x+11y=7) and (3x+5y=4)?
Answer and explanation
Correct answer: Lines intersect at one point
Here, \(a_1=6, b_1=11\) and \(a_2=3, b_2=5\). We have \(a_1/a_2=6/3=2\), whereas \(b_1/b_2=11/5\); the two ratios are unequal. Therefore, the pair is consistent and independent and has a unique solution, so the lines intersect at one point. For parallel or coincident lines, the relevant coefficient ratios must be equal, while perpendicular lines require the product of their slopes to be \(-1\). Exam tip: whenever \(a_1/a_2 \ne b_1/b_2\), conclude that the pair has a unique solution.
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What is the correct answer to this question?
Lines intersect at one point
Why is this the correct answer?
Here, \(a_1=6, b_1=11\) and \(a_2=3, b_2=5\). We have \(a_1/a_2=6/3=2\), whereas \(b_1/b_2=11/5\); the two ratios are unequal. Therefore, the pair is consistent and independent and has a unique solution, so the lines intersect at one point. For parallel or coincident lines, the relevant coefficient ratios must be equal, while perpendicular lines require the product of their slopes to be \(-1\). Exam tip: whenever \(a_1/a_2 \ne b_1/b_2\), conclude that the pair has a unique solution.
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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