Choose the correct option for (4x-5y=1) and (8x-9y=3).
Answer and explanation
Correct answer: One unique solution
Compare the coefficient ratios after writing the equations in standard form: \(\frac{a_1}{a_2}=\frac{4}{8}=\frac{1}{2}\) and \(\frac{b_1}{b_2}=\frac{-5}{-9}=\frac{5}{9}\). Since these ratios are unequal, the two lines intersect at exactly one point, so the pair has a unique solution. Infinitely many solutions or the same line require all corresponding ratios to be equal, while no solution requires \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\). Exam tip: first compare \(a_1/a_2\) and \(b_1/b_2\).
Frequently asked questions
What is the correct answer to this question?
One unique solution
Why is this the correct answer?
Compare the coefficient ratios after writing the equations in standard form: \(\frac{a_1}{a_2}=\frac{4}{8}=\frac{1}{2}\) and \(\frac{b_1}{b_2}=\frac{-5}{-9}=\frac{5}{9}\). Since these ratios are unequal, the two lines intersect at exactly one point, so the pair has a unique solution. Infinitely many solutions or the same line require all corresponding ratios to be equal, while no solution requires \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\). 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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