What is the value of k for no solution in 2x + 3y = 4 and kx + 6y = 11?
Answer and explanation
Correct answer: k = 4
A pair of linear equations has no solution when the coefficient ratios are equal but the constant ratio is different: a1/a2 = b1/b2 ≠ c1/c2. Here, 3/6 = 1/2. Therefore, 2/k must also equal 1/2, which gives k = 4. However, the constant ratio is 4/11, and 4/11 is not equal to 1/2. Thus the lines have equal slopes but different intercepts; they are parallel and never intersect. Therefore, there is no solution and option C is correct. Other listed values do not make the lines parallel.
Frequently asked questions
What is the correct answer to this question?
k = 4
Why is this the correct answer?
A pair of linear equations has no solution when the coefficient ratios are equal but the constant ratio is different: a1/a2 = b1/b2 ≠ c1/c2. Here, 3/6 = 1/2. Therefore, 2/k must also equal 1/2, which gives k = 4. However, the constant ratio is 4/11, and 4/11 is not equal to 1/2. Thus the lines have equal slopes but different intercepts; they are parallel and never intersect. Therefore, there is no solution and option C is correct. Other listed values do not make the lines parallel.
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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