For no solution in (k+1)x+4y=9 and 6x+8y=15, what is k?
Answer and explanation
Correct answer: k=2
The governing concept is the no-solution condition for two linear equations: a₁/a₂=b₁/b₂ but c₁/c₂ must be different. Here the coefficient ratio for y is 4/8=1/2. To make the x-coefficient ratio equal to it, require (k+1)/6=1/2. Multiplying by 6 gives k+1=3, so k=2. For this value, the equations have proportional x- and y-coefficients, but their constants have ratio 9/15=3/5, which is not 1/2. Hence the corresponding lines are distinct and parallel, producing no solution. Therefore option B is correct. The other choices do not make the two variable-coefficient ratios equal, so they do not satisfy the required condition.
Frequently asked questions
What is the correct answer to this question?
k=2
Why is this the correct answer?
The governing concept is the no-solution condition for two linear equations: a₁/a₂=b₁/b₂ but c₁/c₂ must be different. Here the coefficient ratio for y is 4/8=1/2. To make the x-coefficient ratio equal to it, require (k+1)/6=1/2. Multiplying by 6 gives k+1=3, so k=2. For this value, the equations have proportional x- and y-coefficients, but their constants have ratio 9/15=3/5, which is not 1/2. Hence the corresponding lines are distinct and parallel, producing no solution. Therefore option B is correct. The other choices do not make the two variable-coefficient ratios equal, so they do not satisfy the required condition.
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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