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Class 10MathematicsPair of Linear Equations in Two VariablesConditions for solvabilityHardLevel 59
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How do the lines appear on a graph when a pair of linear equations in two variables has infinitely many solutions?

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Answer and explanation

Correct answer: They coincide completely

Infinitely many solutions occur when both equations represent the same line, so every point on it is common. Exam tip: check \(a_1/a_2=b_1/b_2=c_1/c_2\). Distinct parallel lines have no common solution.

Related tags

Linear EquationsInfinitely Many SolutionsCoincident LinesGraphical InterpretationSolvability Conditions

Frequently asked questions

What is the correct answer to this question?

They coincide completely

Why is this the correct answer?

Infinitely many solutions occur when both equations represent the same line, so every point on it is common. Exam tip: check \(a_1/a_2=b_1/b_2=c_1/c_2\). Distinct parallel lines have no common solution.

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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