Which statement is correct about the graph of (14x+21y=49) and (2x+3y=8)?
Answer and explanation
Correct answer: Lines are distinct parallel
For the two equations, the ratios of the coefficients of x and y are equal: 14/2 = 21/3 = 7. However, the ratio of the constant terms is 49/8, which is not equal to 7. Thus, the lines have the same slope but different positions, so they are distinct parallel lines. Exam tip: when a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the pair represents distinct parallel lines.
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What is the correct answer to this question?
Lines are distinct parallel
Why is this the correct answer?
For the two equations, the ratios of the coefficients of x and y are equal: 14/2 = 21/3 = 7. However, the ratio of the constant terms is 49/8, which is not equal to 7. Thus, the lines have the same slope but different positions, so they are distinct parallel lines. Exam tip: when a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the pair represents distinct parallel 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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