If (lx+17y=68) and (20x+34y=139) have no solution, what will be the value of (l)?
Answer and explanation
Correct answer: 10
For two linear equations to have no solution, the condition is \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\). Here, \(\frac{l}{20}=\frac{17}{34}=\frac{1}{2}\), so \(l=10\). Also, \(\frac{68}{139}\ne\frac{1}{2}\), confirming that the lines are parallel and inconsistent. Exam tip: First equate the ratios of the coefficients to find the parameter, and then verify that the ratio of constants is different.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
For two linear equations to have no solution, the condition is \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\). Here, \(\frac{l}{20}=\frac{17}{34}=\frac{1}{2}\), so \(l=10\). Also, \(\frac{68}{139}\ne\frac{1}{2}\), confirming that the lines are parallel and inconsistent. Exam tip: First equate the ratios of the coefficients to find the parameter, and then verify that the ratio of constants 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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