If (lx+15y=60) and (18x+45y=181) have no solution, what will be the value of (l)?
Answer and explanation
Correct answer: 6
For two linear equations to have no solution, the ratios of the coefficients of the variables must be equal, while the ratio of the constant terms must be different. Thus, \(\frac{l}{18}=\frac{15}{45}=\frac{1}{3}\), which gives \(l=6\). Also, \(\frac{60}{181}\neq\frac{1}{3}\), since \(180\neq181\); therefore, the two lines are distinct and parallel. If 5 or 7 were used, the coefficient ratios would not be equal, resulting in a unique solution. Exam tip: For no solution, remember \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\).
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
For two linear equations to have no solution, the ratios of the coefficients of the variables must be equal, while the ratio of the constant terms must be different. Thus, \(\frac{l}{18}=\frac{15}{45}=\frac{1}{3}\), which gives \(l=6\). Also, \(\frac{60}{181}\neq\frac{1}{3}\), since \(180\neq181\); therefore, the two lines are distinct and parallel. If 5 or 7 were used, the coefficient ratios would not be equal, resulting in a unique solution. Exam tip: For no solution, remember \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\).
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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