If (ax+9y=27) and (14x+21y=64) have no solution then what will (a) be?
Answer and explanation
Correct answer: (6)
For two linear equations to have no solution, the ratios of the corresponding coefficients must be equal, while the ratio of the constants must be different. Thus, \(\frac{a}{14}=\frac{9}{21}=\frac{3}{7}\), giving \(a=6\). Also, \(\frac{27}{64}\ne\frac{3}{7}\), so the equations are inconsistent and have no solution. Exam tip: first equate the ratios of the coefficients to find the parameter, then verify that the constants are not in the same ratio.
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 corresponding coefficients must be equal, while the ratio of the constants must be different. Thus, \(\frac{a}{14}=\frac{9}{21}=\frac{3}{7}\), giving \(a=6\). Also, \(\frac{27}{64}\ne\frac{3}{7}\), so the equations are inconsistent and have no solution. Exam tip: first equate the ratios of the coefficients to find the parameter, then verify that the constants are not in the same ratio.
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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