Which ratio relation is correct for (3x+5y-20=0) and (9x+15y-60=0)?
Answer and explanation
Correct answer: \(\frac{3}{9}=\frac{5}{15}=\frac{-20}{-60}\)
For the first equation, \(a_1=3, b_1=5, c_1=-20\), and for the second, \(a_2=9, b_2=15, c_2=-60\). Thus, \(\frac{a_1}{a_2}=\frac{3}{9}=\frac{1}{3}\), \(\frac{b_1}{b_2}=\frac{5}{15}=\frac{1}{3}\), and \(\frac{c_1}{c_2}=\frac{-20}{-60}=\frac{1}{3}\). Since all three ratios are equal, the two lines are coincident and the pair has infinitely many solutions. Exam tip: the condition \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\) indicates infinitely many solutions.
Frequently asked questions
What is the correct answer to this question?
\(\frac{3}{9}=\frac{5}{15}=\frac{-20}{-60}\)
Why is this the correct answer?
For the first equation, \(a_1=3, b_1=5, c_1=-20\), and for the second, \(a_2=9, b_2=15, c_2=-60\). Thus, \(\frac{a_1}{a_2}=\frac{3}{9}=\frac{1}{3}\), \(\frac{b_1}{b_2}=\frac{5}{15}=\frac{1}{3}\), and \(\frac{c_1}{c_2}=\frac{-20}{-60}=\frac{1}{3}\). Since all three ratios are equal, the two lines are coincident and the pair has infinitely many solutions. Exam tip: the condition \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\) indicates infinitely many solutions.
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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