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Class 10MathematicsPair of Linear Equations in Two VariablesConditions for solvabilityEasy
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Which of the following pairs is inconsistent?

Answer and explanation

Correct answer: x + 4y = 6 and 2x + 8y = 13

In option A, \(a_1/a_2=1/2\) and \(b_1/b_2=4/8=1/2\), but \(c_1/c_2=6/13\). Thus, \(a_1/a_2=b_1/b_2\ne c_1/c_2\), so the two lines are distinct and parallel and the pair has no solution. Hence, it is inconsistent. In option C, all three ratios are equal, so the pair is dependent and consistent. Exam tip: For an inconsistent pair, check whether \(a_1/a_2=b_1/b_2\ne c_1/c_2\).

Related tags

Pair Of Linear EquationsConditions For SolvabilityInconsistent PairNo SolutionClass 10 MathematicsPair Of Linear Equations In Two VariablesMathematicsClass 10 Mcq
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10 more MCQs
  1. 1If both lines appear exactly at the same place on the graph, how many solutions will there be?
  2. 2If (a₁/a₂ ≠ b₁/b₂), how will two lines appear on the graph?
  3. 3How many solutions are there for (2x + 5y = 20) and (4x + 10y = 40)?
  4. 4Which pair of equations will give a unique solution?
  5. 5If a₁ = 4, b₁ = 6, c₁ = 10 and a₂ = 2, b₂ = 3, c₂ = 5, how will the lines be related?
  6. 6If a₁ = 6, b₁ = 9, c₁ = 12 and a₂ = 2, b₂ = 3, c₂ = 4, how will the lines be?
  7. 7If a₁ = 7, b₁ = 14, c₁ = 21 and a₂ = 1, b₂ = 2, c₂ = 3, how will the lines be?
  8. 8If the line \(3x+ay=24\) coincides with the line \(3x+4y=24\), what is the value of \(a\)?
  9. 9If the line 4x + ay = 20 is coincident with the line 2x + 3y = 10, what is the value of a?
  10. 10What type of lines are 9x − 6y = 21 and 3x − 2y = 7?
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