If (lx+13y=52) and (14x+26y=109) have no solution, what will be the value of (l)?
Answer and explanation
Correct answer: 7
For two 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. Thus, l/14 = 13/26 = 1/2, giving l = 7. Also, 52/109 is not equal to 1/2, so the two lines are parallel and inconsistent. Exam tip: compare the coefficient ratios first, then verify that the constant-term ratio is different.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
For two 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. Thus, l/14 = 13/26 = 1/2, giving l = 7. Also, 52/109 is not equal to 1/2, so the two lines are parallel and inconsistent. Exam tip: compare the coefficient ratios first, then verify that the constant-term ratio is different.
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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