Which statement is correct for (7x+8y=26) and (14x+15y=51)?
Answer and explanation
Correct answer: 7/14 ≠ 8/15, so there is a unique solution
For the pair, \(a_1/a_2=7/14=1/2\) and \(b_1/b_2=8/15\), and these ratios are unequal. Thus, \(a_1/a_2\ne b_1/b_2\), so the two lines intersect at one point and the equations have a unique solution. Options A and C incorrectly treat the ratios as equal; coincident lines require all corresponding ratios to be equal. Exam tip: first compare \(a_1/a_2\) and \(b_1/b_2\).
Frequently asked questions
What is the correct answer to this question?
7/14 ≠ 8/15, so there is a unique solution
Why is this the correct answer?
For the pair, \(a_1/a_2=7/14=1/2\) and \(b_1/b_2=8/15\), and these ratios are unequal. Thus, \(a_1/a_2\ne b_1/b_2\), so the two lines intersect at one point and the equations have a unique solution. Options A and C incorrectly treat the ratios as equal; coincident lines require all corresponding ratios to be equal. Exam tip: first compare \(a_1/a_2\) and \(b_1/b_2\).
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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