Which relation is correct for (6x+9y=30) and (2x+3y=12)?
Answer and explanation
Correct answer: \(\frac{6}{2}=\frac{9}{3}\ne\frac{30}{12}\)
Compare the ratios of the corresponding coefficients and constants: \(\frac{6}{2}=3\), \(\frac{9}{3}=3\), but \(\frac{30}{12}=2.5\). Therefore, \(\frac{6}{2}=\frac{9}{3}\ne\frac{30}{12}\), so option C is correct. This condition means that the pair of linear equations has no solution: the variable-coefficient ratios are equal, but the constant-term ratio is different. Exam tip: when \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), the pair is inconsistent and has no solution.
Frequently asked questions
What is the correct answer to this question?
\(\frac{6}{2}=\frac{9}{3}\ne\frac{30}{12}\)
Why is this the correct answer?
Compare the ratios of the corresponding coefficients and constants: \(\frac{6}{2}=3\), \(\frac{9}{3}=3\), but \(\frac{30}{12}=2.5\). Therefore, \(\frac{6}{2}=\frac{9}{3}\ne\frac{30}{12}\), so option C is correct. This condition means that the pair of linear equations has no solution: the variable-coefficient ratios are equal, but the constant-term ratio is different. Exam tip: when \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\), 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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