What will (a) be for (3x+4y=10) and (6x+ay=25) to have no solution?
Answer and explanation
Correct answer: 8
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, \(\frac{3}{6}=\frac{1}{2}\) and \(\frac{10}{25}=\frac{2}{5}\), so the constant-term ratio is different. Therefore, set \(\frac{4}{a}=\frac{3}{6}=\frac{1}{2}\), which gives \(a=8\). Hence, option C is correct. Exam tip: First equate the ratios of the coefficients of the variables, then verify that the ratio of constants is different.
Frequently asked questions
What is the correct answer to this question?
8
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, \(\frac{3}{6}=\frac{1}{2}\) and \(\frac{10}{25}=\frac{2}{5}\), so the constant-term ratio is different. Therefore, set \(\frac{4}{a}=\frac{3}{6}=\frac{1}{2}\), which gives \(a=8\). Hence, option C is correct. Exam tip: First equate the ratios of the coefficients of the variables, 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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