What will (k) be for (6x+ky=42) and (2x+5y=14) to have infinitely many solutions?
Answer and explanation
Correct answer: 15
For two linear equations to have infinitely many solutions, the condition is \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\). Here, \(\frac{6}{2}=3\) and \(\frac{42}{14}=3\), so \(\frac{k}{5}=3\), giving \(k=15\). Therefore, option B is correct. With option C, \(k=18\), the ratio \(\frac{k}{5}\) is not 3, so the equations do not represent the same line. Exam tip: For infinitely many solutions, check that all three corresponding ratios are equal.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
For two linear equations to have infinitely many solutions, the condition is \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\). Here, \(\frac{6}{2}=3\) and \(\frac{42}{14}=3\), so \(\frac{k}{5}=3\), giving \(k=15\). Therefore, option B is correct. With option C, \(k=18\), the ratio \(\frac{k}{5}\) is not 3, so the equations do not represent the same line. Exam tip: For infinitely many solutions, check that all three corresponding ratios are equal.
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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