What is the correct solution status for (4x-7y=3) and (8x-13y=6)?
Answer and explanation
Correct answer: One unique solution
For the two equations, \(a_1=4, b_1=-7, a_2=8, b_2=-13\). Here, \(\frac{a_1}{a_2}=\frac{4}{8}=\frac{1}{2}\), whereas \(\frac{b_1}{b_2}=\frac{-7}{-13}=\frac{7}{13}\); the two ratios are unequal. Therefore, the lines intersect at exactly one point, so the system has one unique solution. Exam tip: If \(\frac{a_1}{a_2}\ne\frac{b_1}{b_2}\), a pair of linear equations has a unique solution.
Frequently asked questions
What is the correct answer to this question?
One unique solution
Why is this the correct answer?
For the two equations, \(a_1=4, b_1=-7, a_2=8, b_2=-13\). Here, \(\frac{a_1}{a_2}=\frac{4}{8}=\frac{1}{2}\), whereas \(\frac{b_1}{b_2}=\frac{-7}{-13}=\frac{7}{13}\); the two ratios are unequal. Therefore, the lines intersect at exactly one point, so the system has one unique solution. Exam tip: If \(\frac{a_1}{a_2}\ne\frac{b_1}{b_2}\), a pair of linear equations has a unique solution.
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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