Which ratio relation is correct for (2x+3y-11=0) and (6x+9y-33=0)?
Answer and explanation
Correct answer: \(\frac{2}{6}=\frac{3}{9}=\frac{-11}{-33}\)
For the first equation, a₁=2, b₁=3 and c₁=-11; for the second, a₂=6, b₂=9 and c₂=-33. Thus, \(\frac{a_1}{a_2}=\frac{2}{6}=\frac{1}{3}\), \(\frac{b_1}{b_2}=\frac{3}{9}=\frac{1}{3}\), and \(\frac{c_1}{c_2}=\frac{-11}{-33}=\frac{1}{3}\). Therefore, option C gives the correct relation. The second equation is three times the first, so the two lines are coincident and the pair has infinitely many solutions. Exam tip: Equal values of all three ratios indicate infinitely many solutions.
Frequently asked questions
What is the correct answer to this question?
\(\frac{2}{6}=\frac{3}{9}=\frac{-11}{-33}\)
Why is this the correct answer?
For the first equation, a₁=2, b₁=3 and c₁=-11; for the second, a₂=6, b₂=9 and c₂=-33. Thus, \(\frac{a_1}{a_2}=\frac{2}{6}=\frac{1}{3}\), \(\frac{b_1}{b_2}=\frac{3}{9}=\frac{1}{3}\), and \(\frac{c_1}{c_2}=\frac{-11}{-33}=\frac{1}{3}\). Therefore, option C gives the correct relation. The second equation is three times the first, so the two lines are coincident and the pair has infinitely many solutions. Exam tip: Equal values of all three ratios indicate 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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