Which statement is correct by observing (12x+5y=41) and (24x+10y=82)?
Answer and explanation
Correct answer: Lines are the same
The second equation is exactly twice the first: 24x+10y=2(12x+5y) and 82=2×41. Therefore, both equations represent the same line and the pair has infinitely many solutions. Option A would be correct if the ratios of the coefficients of x and y were equal but the ratio of the constants were different. In an exam, compare a₁/a₂, b₁/b₂, and c₁/c₂ to determine the position of the lines.
Frequently asked questions
What is the correct answer to this question?
Lines are the same
Why is this the correct answer?
The second equation is exactly twice the first: 24x+10y=2(12x+5y) and 82=2×41. Therefore, both equations represent the same line and the pair has infinitely many solutions. Option A would be correct if the ratios of the coefficients of x and y were equal but the ratio of the constants were different. In an exam, compare a₁/a₂, b₁/b₂, and c₁/c₂ to determine the position of the 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: Conditions for solvability.
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