What is the value of (b) for the equations (bx+9y=36) and (16x+24y=97) to have no solution?
Answer and explanation
Correct answer: 6
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, \(\frac{b}{16}=\frac{9}{24}=\frac{3}{8}\), giving \(b=6\). Also, \(\frac{36}{97}\ne\frac{3}{8}\), so the two lines are distinct and parallel. Exam tip: For ‘no solution’, first equate the ratios of the coefficients of the variables, then verify that the constants’ ratio is different.
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 condition is \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\). Here, \(\frac{b}{16}=\frac{9}{24}=\frac{3}{8}\), giving \(b=6\). Also, \(\frac{36}{97}\ne\frac{3}{8}\), so the two lines are distinct and parallel. Exam tip: For ‘no solution’, first equate the ratios of the coefficients of the variables, then verify that the constants’ ratio 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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