If 8x − 4y = 24 and 2x − y = t are inconsistent, what is the correct condition for t?
Answer and explanation
Correct answer: t ≠ 6
Compare the coefficients in 8x − 4y = 24 and 2x − y = t. The x-coefficient ratio is 8/2 = 4, and the y-coefficient ratio is (−4)/(−1) = 4. Thus the two lines have the same direction. For inconsistency, the constant ratio must not equal 4. The constant ratio is 24/t, so we require 24/t ≠ 4. The equality 24/t = 4 gives t = 6; in that case the second equation is one-fourth of the first and the equations represent the same line with infinitely many solutions. Hence the inconsistent condition is t ≠ 6, making option B correct.
Frequently asked questions
What is the correct answer to this question?
t ≠ 6
Why is this the correct answer?
Compare the coefficients in 8x − 4y = 24 and 2x − y = t. The x-coefficient ratio is 8/2 = 4, and the y-coefficient ratio is (−4)/(−1) = 4. Thus the two lines have the same direction. For inconsistency, the constant ratio must not equal 4. The constant ratio is 24/t, so we require 24/t ≠ 4. The equality 24/t = 4 gives t = 6; in that case the second equation is one-fourth of the first and the equations represent the same line with infinitely many solutions. Hence the inconsistent condition is t ≠ 6, making option B correct.
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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