How many solutions will the equations (9x+5y=41) and (18x+10y=85) have?
Answer and explanation
Correct answer: No solution
Here, \(\frac{a_1}{a_2}=\frac{9}{18}=\frac{1}{2}\) and \(\frac{b_1}{b_2}=\frac{5}{10}=\frac{1}{2}\), but \(\frac{c_1}{c_2}=\frac{41}{85}\neq\frac{1}{2}\). Thus, the two lines are parallel and distinct, so the pair has no solution. Option B is incorrect because infinitely many solutions require all three ratios to be equal. Exam tip: when \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\), the pair is inconsistent and has no solution.
Frequently asked questions
What is the correct answer to this question?
No solution
Why is this the correct answer?
Here, \(\frac{a_1}{a_2}=\frac{9}{18}=\frac{1}{2}\) and \(\frac{b_1}{b_2}=\frac{5}{10}=\frac{1}{2}\), but \(\frac{c_1}{c_2}=\frac{41}{85}\neq\frac{1}{2}\). Thus, the two lines are parallel and distinct, so the pair has no solution. Option B is incorrect because infinitely many solutions require all three ratios to be equal. Exam tip: when \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\), the pair is inconsistent and has no 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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