Which conclusion is correct for (16x-8y=24) and (2x-y=4)?
Answer and explanation
Correct answer: No solution
Dividing the first equation by 8 gives 2x-y=3, whereas the second equation is 2x-y=4. The ratios of the coefficients of x and y are equal, 16/2 = (-8)/(-1), but the ratio of the constant terms is different. Thus, the two lines are parallel and distinct, so they have no common solution. Exam tip: If a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the pair of linear equations is inconsistent and has no solution.
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What is the correct answer to this question?
No solution
Why is this the correct answer?
Dividing the first equation by 8 gives 2x-y=3, whereas the second equation is 2x-y=4. The ratios of the coefficients of x and y are equal, 16/2 = (-8)/(-1), but the ratio of the constant terms is different. Thus, the two lines are parallel and distinct, so they have no common solution. Exam tip: If a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the pair of linear equations is inconsistent and has 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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