If 6x − 2y = 18 and 3x − y = t are inconsistent, what is the correct condition for t?
Answer and explanation
Correct answer: t ≠ 9
Write the equations in comparable coefficient form: 6x − 2y = 18 and 3x − y = t. The coefficient ratios are 6/3 = 2 and (−2)/(−1) = 2. For the pair to be inconsistent, the constant ratio must differ from these equal coefficient ratios. The constant ratio is 18/t, so inconsistency requires 18/t ≠ 2. If t = 9, then 18/t = 2 and the second equation is exactly half of the first, giving infinitely many solutions rather than inconsistency. Therefore t must not equal 9, so option B is correct. The other numerical choices do not express the required general condition.
Frequently asked questions
What is the correct answer to this question?
t ≠ 9
Why is this the correct answer?
Write the equations in comparable coefficient form: 6x − 2y = 18 and 3x − y = t. The coefficient ratios are 6/3 = 2 and (−2)/(−1) = 2. For the pair to be inconsistent, the constant ratio must differ from these equal coefficient ratios. The constant ratio is 18/t, so inconsistency requires 18/t ≠ 2. If t = 9, then 18/t = 2 and the second equation is exactly half of the first, giving infinitely many solutions rather than inconsistency. Therefore t must not equal 9, so option B is correct. The other numerical choices do not express the required general 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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