What will (k) be for infinitely many solutions of (3x+ky=12) and (6x+8y=24)?
Answer and explanation
Correct answer: 4
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, \(\frac{3}{6}=\frac{12}{24}=\frac{1}{2}\), so \(\frac{k}{8}=\frac{1}{2}\), giving \(k=4\). Therefore, option B is correct. Exam tip: infinitely many solutions require all three corresponding ratios to be equal, not just two of them.
Frequently asked questions
What is the correct answer to this question?
4
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, \(\frac{3}{6}=\frac{12}{24}=\frac{1}{2}\), so \(\frac{k}{8}=\frac{1}{2}\), giving \(k=4\). Therefore, option B is correct. Exam tip: infinitely many solutions require all three corresponding ratios to be equal, not just two of them.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
