Which statement is correct for the equations (8x+9y=37) and (16x+17y=73)?
Answer and explanation
Correct answer: \(\frac{8}{16}\ne\frac{9}{17}\), so there is one unique solution
Here, \(\frac{a_1}{a_2}=\frac{8}{16}=\frac{1}{2}\), whereas \(\frac{b_1}{b_2}=\frac{9}{17}\). Since these two ratios are unequal, the two lines intersect at exactly one point, so the pair has a unique solution. Option A describes the case of parallel distinct lines, which does not apply here. Exam tip: first compare \(\frac{a_1}{a_2}\) and \(\frac{b_1}{b_2}\); if they are unequal, the pair has a unique solution.
Frequently asked questions
What is the correct answer to this question?
\(\frac{8}{16}\ne\frac{9}{17}\), so there is one unique solution
Why is this the correct answer?
Here, \(\frac{a_1}{a_2}=\frac{8}{16}=\frac{1}{2}\), whereas \(\frac{b_1}{b_2}=\frac{9}{17}\). Since these two ratios are unequal, the two lines intersect at exactly one point, so the pair has a unique solution. Option A describes the case of parallel distinct lines, which does not apply here. Exam tip: first compare \(\frac{a_1}{a_2}\) and \(\frac{b_1}{b_2}\); if they are unequal, the pair 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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