Which ratio relation is correct for the equations (8x+13y-59=0) and (24x+39y-177=0)?
Answer and explanation
Correct answer: (8/24=13/39=(-59)/(-177))
Check the three ratios: \(a_1/a_2=8/24=1/3\), \(b_1/b_2=13/39=1/3\), and \(c_1/c_2=(-59)/(-177)=1/3\). Thus, \(a_1/a_2=b_1/b_2=c_1/c_2\); the two lines are coincident and the pair has infinitely many solutions. Options A and D incorrectly state that one ratio is unequal. Exam tip: if all three ratios are equal, there are infinitely many solutions; if only the first two are equal and the third differs, there is no solution.
Frequently asked questions
What is the correct answer to this question?
(8/24=13/39=(-59)/(-177))
Why is this the correct answer?
Check the three ratios: \(a_1/a_2=8/24=1/3\), \(b_1/b_2=13/39=1/3\), and \(c_1/c_2=(-59)/(-177)=1/3\). Thus, \(a_1/a_2=b_1/b_2=c_1/c_2\); the two lines are coincident and the pair has infinitely many solutions. Options A and D incorrectly state that one ratio is unequal. Exam tip: if all three ratios are equal, there are infinitely many solutions; if only the first two are equal and the third differs, there is no 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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