If (lx+11y=44) and (10x+22y=91) have no solution then what will be the value of (l)?
Answer and explanation
Correct answer: 5
For two linear equations to have no solution, the condition is \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\). Here, \(\frac{l}{10}=\frac{11}{22}=\frac{1}{2}\), so \(l=5\). Also, \(\frac{44}{91}\neq\frac{1}{2}\), confirming that the two lines are parallel and distinct. Exam tip: For ‘no solution’, first equate the ratios of the coefficients and then check that the ratio of constants is different.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
For two linear equations to have no solution, the condition is \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\). Here, \(\frac{l}{10}=\frac{11}{22}=\frac{1}{2}\), so \(l=5\). Also, \(\frac{44}{91}\neq\frac{1}{2}\), confirming that the two lines are parallel and distinct. Exam tip: For ‘no solution’, first equate the ratios of the coefficients and then check 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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