Question

please solve it 15th .

Answer 1

Heya dear,
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●For no solution

$\frac{ a1}{a2} = \frac{b1}{b2} \: is \: not \: equal \: to \: \frac{c1}{c2}$


Here,

$\frac{2}{ 3 } = \frac{k}{ -5 } \: is \: not \: equal \: to \: \frac{1}{7} \\ \frac{2}{3} = \frac{k}{ - 5} \: \: \: and \: \: \: \frac{k}{ - 5} \: is \: not \: equal \: to \: \frac{1}{7} \\ k = \frac{ - 10}{3} \: \: \: and \: \: \: k \: is \: not \: equal \: to \: \frac{ - 5}{7}$


Hence for  k = -10/3 the system of equation has no solution


●For infinitely many solution

$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}$


Here,

$\frac{2}{3} = \frac{k}{ - 5} \: is \: not \: equal \: to \: \frac{1}{7} \\ = > k = \frac{ - 10}{3}$


But since here 
$\frac{k}{ - 5} \: i \: not \: equal \: to \: \frac{1}{7} \: (as \: k \: = \frac{ - 10}{3} )$


Hence the system does not have infinitely many solutions.

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