If a₁/a₂ = b₁/b₂ ≠ c₁/c₂, what is the position of the two lines?
Answer and explanation
Correct answer: Parallel and distinct
For the pair of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, the graphical classification uses the coefficient ratios. If a₁/a₂ = b₁/b₂ but this common ratio is different from c₁/c₂, the x- and y-coefficients are proportional while the constant terms are not. The equations therefore have the same slope but different intercepts. Their graphs are distinct parallel lines and have no common solution, so option B is correct. Coincident lines require all three ratios to be equal, while intersecting lines require the first two ratios to be unequal. Meeting at the origin is not implied by this ratio condition.
Frequently asked questions
What is the correct answer to this question?
Parallel and distinct
Why is this the correct answer?
For the pair of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, the graphical classification uses the coefficient ratios. If a₁/a₂ = b₁/b₂ but this common ratio is different from c₁/c₂, the x- and y-coefficients are proportional while the constant terms are not. The equations therefore have the same slope but different intercepts. Their graphs are distinct parallel lines and have no common solution, so option B is correct. Coincident lines require all three ratios to be equal, while intersecting lines require the first two ratios to be unequal. Meeting at the origin is not implied by this ratio condition.
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..
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