Muft Shiksha
Update

Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है

Subjects
Class 10MathematicsPair of Linear Equations in Two VariablesConditions for solvabilityEasy
0 reads0 ratings0 helpful

Which option is correct for (6x+11y=7) and (3x+5y=4)?

Answer and explanation

Correct answer: Lines intersect at one point

Here, \(a_1=6, b_1=11\) and \(a_2=3, b_2=5\). We have \(a_1/a_2=6/3=2\), whereas \(b_1/b_2=11/5\); the two ratios are unequal. Therefore, the pair is consistent and independent and has a unique solution, so the lines intersect at one point. For parallel or coincident lines, the relevant coefficient ratios must be equal, while perpendicular lines require the product of their slopes to be \(-1\). Exam tip: whenever \(a_1/a_2 \ne b_1/b_2\), conclude that the pair has a unique solution.

Related tags

Linear EquationsSolvability ConditionsUnique SolutionIntersecting LinesConditions For SolvabilityPair Of Linear Equations In Two VariablesMathematicsClass 10 Mcq
सुधार सुझाएँ / Earn

Was this question useful?

No ratings yetWrite a review / Rate this question

Student Reviews

No published reviews yet.

KEEP PRACTISING

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?
Found an issue? Help improve this questionMy reports and replies

Add Muft Shiksha to your Home Screen

In Safari, tap Share, then Add to Home Screen.