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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.

Related tags

Linear EquationsSolvability ConditionsRatio Of CoefficientsCoincident LinesInfinitely Many SolutionsConditions For SolvabilityPair Of Linear Equations In Two VariablesMathematics

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