If (a₁/a₂ ≠ b₁/b₂), how will two lines appear on the graph?
Answer and explanation
Correct answer: Intersecting at one point
For the pair of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, the ratios of corresponding coefficients classify the graphs. If a₁/a₂ is not equal to b₁/b₂, the coefficients of x and y are not proportional in the same way. Consequently, the two lines have different slopes and must meet at exactly one point, producing a unique solution. Therefore option C is correct. Parallel lines occur when a₁/a₂ = b₁/b₂ but this common ratio is not equal to c₁/c₂. Coincident lines occur when all three ratios are equal. The condition given here rules out both of those cases, so the lines are intersecting rather than parallel or coincident.
Frequently asked questions
What is the correct answer to this question?
Intersecting at one point
Why is this the correct answer?
For the pair of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, the ratios of corresponding coefficients classify the graphs. If a₁/a₂ is not equal to b₁/b₂, the coefficients of x and y are not proportional in the same way. Consequently, the two lines have different slopes and must meet at exactly one point, producing a unique solution. Therefore option C is correct. Parallel lines occur when a₁/a₂ = b₁/b₂ but this common ratio is not equal to c₁/c₂. Coincident lines occur when all three ratios are equal. The condition given here rules out both of those cases, so the lines are intersecting rather than parallel or coincident.
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.
