What is the relation among all three ratios in the equations (8x+12y=40) and (2x+3y=10)?
Answer and explanation
Correct answer: All three ratios are equal
Here, a₁/a₂ = 8/2 = 4, b₁/b₂ = 12/3 = 4, and c₁/c₂ = 40/10 = 4. Hence, a₁/a₂ = b₁/b₂ = c₁/c₂, so all three ratios are equal. This means that the two equations represent the same line and have infinitely many solutions. Option B is incorrect because the third ratio is not different; it is also equal to 4. Exam tip: when all three ratios are equal, the pair of linear equations represents coincident lines and has infinitely many solutions.
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 = 8/2 = 4, b₁/b₂ = 12/3 = 4, and c₁/c₂ = 40/10 = 4. Hence, a₁/a₂ = b₁/b₂ = c₁/c₂, so all three ratios are equal. This means that the two equations represent the same line and have infinitely many solutions. Option B is incorrect because the third ratio is not different; it is also equal to 4. Exam tip: when all three ratios are equal, the pair of linear equations represents coincident lines and has 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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