Which statement is correct for (6x+7y=23) and (12x+13y=45)?
Answer and explanation
Correct answer: \(\frac{6}{12}\ne\frac{7}{13}\), so there is a unique solution
Here, \(a_1=6, a_2=12, b_1=7, b_2=13\). Thus, \(\frac{a_1}{a_2}=\frac{6}{12}=\frac{1}{2}\), whereas \(\frac{b_1}{b_2}=\frac{7}{13}\); the two ratios are unequal. For a pair of linear equations, the condition \(\frac{a_1}{a_2}\ne\frac{b_1}{b_2}\) indicates a unique solution. In fact, solving the equations gives \(y=1\) and \(x=8/3\), so the value \(y=2\) in option A is incorrect. In an exam, compare the ratios of the coefficients of x and y first; if they are unequal, the pair has a unique solution.
Frequently asked questions
What is the correct answer to this question?
\(\frac{6}{12}\ne\frac{7}{13}\), so there is a unique solution
Why is this the correct answer?
Here, \(a_1=6, a_2=12, b_1=7, b_2=13\). Thus, \(\frac{a_1}{a_2}=\frac{6}{12}=\frac{1}{2}\), whereas \(\frac{b_1}{b_2}=\frac{7}{13}\); the two ratios are unequal. For a pair of linear equations, the condition \(\frac{a_1}{a_2}\ne\frac{b_1}{b_2}\) indicates a unique solution. In fact, solving the equations gives \(y=1\) and \(x=8/3\), so the value \(y=2\) in option A is incorrect. In an exam, compare the ratios of the coefficients of x and y first; 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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