If a₁/a₂ ≠ b₁/b₂, how many solutions will the pair have graphically?
Answer and explanation
Correct answer: Exactly one solution
For the pair a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, the condition a₁/a₂ ≠ b₁/b₂ means that the two lines have different slopes. Lines with different slopes cannot remain parallel or coincide; they intersect at exactly one point. That common point gives the single ordered-pair solution of the equations. Thus option B is correct, and the pair is called consistent and independent. Option A describes parallel distinct lines, generally associated with equal coefficient ratios but an unequal constant ratio. Option C describes coincident lines, where all three ratios are equal, and option D is impossible for two distinct straight lines.
Frequently asked questions
What is the correct answer to this question?
Exactly one solution
Why is this the correct answer?
For the pair a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, the condition a₁/a₂ ≠ b₁/b₂ means that the two lines have different slopes. Lines with different slopes cannot remain parallel or coincide; they intersect at exactly one point. That common point gives the single ordered-pair solution of the equations. Thus option B is correct, and the pair is called consistent and independent. Option A describes parallel distinct lines, generally associated with equal coefficient ratios but an unequal constant ratio. Option C describes coincident lines, where all three ratios are equal, and option D is impossible for two distinct straight lines.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Graphical method of finding solutions..
