What value of (k) makes (2x+3y=7) and (4x+ky=14) have infinitely many solutions?
Answer and explanation
Correct answer: 6
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, \(\frac{2}{4}=\frac{7}{14}=\frac{1}{2}\), so \(\frac{3}{k}=\frac{1}{2}\). Cross-multiplication gives \(k=6\), so option B is correct. Exam tip: for infinitely many solutions, all three coefficient-to-constant ratios must be equal; equality of only two ratios is not sufficient.
Frequently asked questions
What is the correct answer to this question?
6
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, \(\frac{2}{4}=\frac{7}{14}=\frac{1}{2}\), so \(\frac{3}{k}=\frac{1}{2}\). Cross-multiplication gives \(k=6\), so option B is correct. Exam tip: for infinitely many solutions, all three coefficient-to-constant ratios must be equal; equality of only two ratios is not sufficient.
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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