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Class 10MathematicsPair of Linear Equations in Two VariablesConditions for solvabilityHardLevel 60
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Which condition ensures that the pair of linear equations \(a_1x+b_1y=c_1\) and \(a_2x+b_2y=c_2\) has exactly one solution?

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Answer and explanation

Correct answer: \(a_1b_2\ne a_2b_1\)

\(a_1b_2\ne a_2b_1\) makes the lines non-parallel, so they meet once. In option B, proportional coefficients with unequal constants give no solution. Exam tip: compare cross-products.

Related tags

Pair Of Linear EquationsSolvability ConditionsUnique SolutionDeterminantGrade 10 Mathematics

Frequently asked questions

What is the correct answer to this question?

\(a_1b_2\ne a_2b_1\)

Why is this the correct answer?

\(a_1b_2\ne a_2b_1\) makes the lines non-parallel, so they meet once. In option B, proportional coefficients with unequal constants give no solution. Exam tip: compare cross-products.

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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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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