If (lx+7y=21) and (6x+14y=40) have no solution, what will be the value of (l)?
Answer and explanation
Correct answer: 3
For a pair of linear equations to have no solution, the ratios of the coefficients of x and y must be equal, while the ratio of the constant terms must be different. Here, l/6 = 7/14 = 1/2, so l = 3. Also, 21/40 is not equal to 1/2, so the two lines are parallel and distinct. Exam tip: no solution occurs when a₁/a₂ = b₁/b₂ ≠ c₁/c₂.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
For a pair of linear equations to have no solution, the ratios of the coefficients of x and y must be equal, while the ratio of the constant terms must be different. Here, l/6 = 7/14 = 1/2, so l = 3. Also, 21/40 is not equal to 1/2, so the two lines are parallel and distinct. Exam tip: no solution occurs when a₁/a₂ = b₁/b₂ ≠ c₁/c₂.
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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