If (16x-8y=64) and (2x-y=t) are inconsistent, what is the correct condition for (t)?
Answer and explanation
Correct answer: \(t\ne 8\)
Dividing the first equation by 8 gives \(2x-y=8\). Thus, the left-hand sides of the two equations are identical. If \(t=8\), both equations represent the same line and have infinitely many solutions. For the equations to be inconsistent, their right-hand sides must differ; hence, \(t\ne 8\). Exam tip: identical left-hand sides with different right-hand sides imply no solution.
Frequently asked questions
What is the correct answer to this question?
\(t\ne 8\)
Why is this the correct answer?
Dividing the first equation by 8 gives \(2x-y=8\). Thus, the left-hand sides of the two equations are identical. If \(t=8\), both equations represent the same line and have infinitely many solutions. For the equations to be inconsistent, their right-hand sides must differ; hence, \(t\ne 8\). Exam tip: identical left-hand sides with different right-hand sides imply no solution.
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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