What is the relation among all three ratios in (5x+6y=32) and (15x+18y=96)?
Answer and explanation
Correct answer: All three ratios are equal
Here, a₁/a₂ = 5/15 = 1/3, b₁/b₂ = 6/18 = 1/3, and c₁/c₂ = 32/96 = 1/3. Hence, all three ratios are equal, so the two equations represent coincident lines and have infinitely many solutions. In an exam, compare a₁/a₂, b₁/b₂, and c₁/c₂ in that order for equations written as ax + by + c = 0.
Frequently asked questions
What is the correct answer to this question?
All three ratios are equal
Why is this the correct answer?
Here, a₁/a₂ = 5/15 = 1/3, b₁/b₂ = 6/18 = 1/3, and c₁/c₂ = 32/96 = 1/3. Hence, all three ratios are equal, so the two equations represent coincident lines and have infinitely many solutions. In an exam, compare a₁/a₂, b₁/b₂, and c₁/c₂ in that order for equations written as ax + by + c = 0.
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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