What type of pair is formed by the equations (13x+4y=39) and (6x+2y=17)?
Answer and explanation
Correct answer: Consistent and independent
The ratios of the coefficients of x and y are unequal: 13/6 ≠ 4/2. Therefore, the two lines intersect at exactly one point, giving a unique solution. Hence, the pair is consistent and independent. Options A and D describe parallel-line cases, while option B would require infinitely many solutions. Exam tip: If a₁/a₂ ≠ b₁/b₂, the pair of linear equations is consistent and independent.
Frequently asked questions
What is the correct answer to this question?
Consistent and independent
Why is this the correct answer?
The ratios of the coefficients of x and y are unequal: 13/6 ≠ 4/2. Therefore, the two lines intersect at exactly one point, giving a unique solution. Hence, the pair is consistent and independent. Options A and D describe parallel-line cases, while option B would require infinitely many solutions. Exam tip: If a₁/a₂ ≠ b₁/b₂, the pair of linear equations is consistent and independent.
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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