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Class-10»Maths

For what value of k, the following system of equations has (i) a unique solution (ii) no solution : 2x+ky=1, 3x-5y=7?

$T h e g i v e n e q u a t i o n b e a s, 2 x + k y = 1 ...... (1) 3 x - 5 y = 7 ....... (2) F o r u n i q u e s o l u t i o n, \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} \Rightarrow \frac{2}{3} \neq \frac{k}{- 5} \Rightarrow k \neq - \frac{10}{3} H e n c e, f o r u n i q u e s o l u t i o n k s h o u l d n o t b e - \frac{10}{3} . F o r n o s o l u t i o n, \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}} \Rightarrow \frac{2}{3} = \frac{k}{- 5} \neq \frac{1}{7} \Rightarrow \frac{2}{3} = \frac{k}{- 5} (b e c a u s e, \frac{2}{3} \neq \frac{1}{7}) \Rightarrow k = - \frac{10}{3} H e n c e, f o r n o s o l u t i o n k s h o u l d b e - \frac{10}{3}$

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