What will (k) be for (2x+3y=9) and (4x+ky=18) to have infinitely many solutions?
Answer and explanation
Correct answer: 6
For two linear equations to have infinitely many solutions, the ratios of corresponding coefficients and constants must be equal: a₁/a₂ = b₁/b₂ = c₁/c₂. Here, 2/4 = 9/18 = 1/2, so 3/k = 1/2, which gives k = 6. Therefore, option C is correct. Exam tip: For infinitely many solutions, always check a₁/a₂ = b₁/b₂ = c₁/c₂.
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 ratios of corresponding coefficients and constants must be equal: a₁/a₂ = b₁/b₂ = c₁/c₂. Here, 2/4 = 9/18 = 1/2, so 3/k = 1/2, which gives k = 6. Therefore, option C is correct. Exam tip: For infinitely many solutions, always check a₁/a₂ = b₁/b₂ = c₁/c₂.
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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