What type of pair is (13x+4y=39) and (6x+2y=17)?
Answer and explanation
Correct answer: Consistent and independent
For a pair of linear equations, if \(\frac{a_1}{a_2} \ne \frac{b_1}{b_2}\), the pair has a unique solution and is called consistent and independent. Here, \(\frac{13}{6} \ne \frac{4}{2}\), so the two lines intersect at exactly one point. Therefore, option C is correct. Option B would require infinitely many solutions, which occurs only when \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\). Exam tip: first compare \(a_1/a_2\) and \(b_1/b_2\).
Frequently asked questions
What is the correct answer to this question?
Consistent and independent
Why is this the correct answer?
For a pair of linear equations, if \(\frac{a_1}{a_2} \ne \frac{b_1}{b_2}\), the pair has a unique solution and is called consistent and independent. Here, \(\frac{13}{6} \ne \frac{4}{2}\), so the two lines intersect at exactly one point. Therefore, option C is correct. Option B would require infinitely many solutions, which occurs only when \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\). Exam tip: first compare \(a_1/a_2\) and \(b_1/b_2\).
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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