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Class 10MathematicsPair of Linear Equations in Two VariablesConditions for solvabilityExpertLevel 59
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If coefficient ratios are equal and the constant ratio is different in a pair, what is the solution status?

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Answer and explanation

Correct answer: No solution

For a pair of linear equations, if \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), the two lines have the same slope but different intercepts. Hence, they are distinct parallel lines and never intersect, so the pair has no solution and is inconsistent. Exam tip: equal coefficient ratios with an unequal constant-term ratio indicate “no solution” immediately.

Related tags

Class10Linear EquationsSolvabilityParallel LinesInconsistent Pair

Frequently asked questions

What is the correct answer to this question?

No solution

Why is this the correct answer?

For a pair of linear equations, if \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), the two lines have the same slope but different intercepts. Hence, they are distinct parallel lines and never intersect, so the pair has no solution and is inconsistent. Exam tip: equal coefficient ratios with an unequal constant-term ratio indicate “no solution” immediately.

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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