What is the correct solution status for the equations (11x+6y=25) and (22x+12y=53)?
Answer and explanation
Correct answer: Inconsistent; two distinct parallel lines
For the two equations, \(\frac{a_1}{a_2}=\frac{11}{22}=\frac{1}{2}\) and \(\frac{b_1}{b_2}=\frac{6}{12}=\frac{1}{2}\), but \(\frac{c_1}{c_2}=\frac{25}{53}\neq\frac{1}{2}\). Thus, \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\), which represents an inconsistent pair of equations and two distinct parallel lines. Therefore, there is no solution. Option C would be correct only if all three ratios were equal. Exam tip: compare the ratios in the order \(a_1/a_2\), \(b_1/b_2\), and then \(c_1/c_2\).
Frequently asked questions
What is the correct answer to this question?
Inconsistent; two distinct parallel lines
Why is this the correct answer?
For the two equations, \(\frac{a_1}{a_2}=\frac{11}{22}=\frac{1}{2}\) and \(\frac{b_1}{b_2}=\frac{6}{12}=\frac{1}{2}\), but \(\frac{c_1}{c_2}=\frac{25}{53}\neq\frac{1}{2}\). Thus, \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\), which represents an inconsistent pair of equations and two distinct parallel lines. Therefore, there is no solution. Option C would be correct only if all three ratios were equal. Exam tip: compare the ratios in the order \(a_1/a_2\), \(b_1/b_2\), and then \(c_1/c_2\).
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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