What is the value of (a) for (ax+2y=5) and (6x+4y=13) to have no solution?
Answer and explanation
Correct answer: 3
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, \(\frac{a}{6}=\frac{2}{4}=\frac{1}{2}\), while \(\frac{5}{13}\ne\frac{1}{2}\). Hence, \(a=3\). With the other options, the coefficient ratios are unequal, so the equations have a unique solution. Exam tip: first equate the ratios of the coefficients of x and y, then compare that ratio with the constants.
Frequently asked questions
What is the correct answer to this question?
3
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, \(\frac{a}{6}=\frac{2}{4}=\frac{1}{2}\), while \(\frac{5}{13}\ne\frac{1}{2}\). Hence, \(a=3\). With the other options, the coefficient ratios are unequal, so the equations have a unique solution. Exam tip: first equate the ratios of the coefficients of x and y, then compare that ratio with the constants.
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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