What is the relation among all three ratios in the equations (7x+10y=46) and (21x+30y=138)?
Answer and explanation
Correct answer: All three ratios are equal
The three ratios are 7/21=1/3, 10/30=1/3, and 46/138=1/3. Thus, a₁/a₂=b₁/b₂=c₁/c₂. Therefore, the two linear equations represent the same line and the pair has infinitely many solutions. Exam tip: when all three ratios are equal, the equations are coincident.
Frequently asked questions
What is the correct answer to this question?
All three ratios are equal
Why is this the correct answer?
The three ratios are 7/21=1/3, 10/30=1/3, and 46/138=1/3. Thus, a₁/a₂=b₁/b₂=c₁/c₂. Therefore, the two linear equations represent the same line and the pair has infinitely many solutions. Exam tip: when all three ratios are equal, the equations are coincident.
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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