Find the value of k for which each of the following systems of equations has no solution:

$8 x + 5 y = 9, k x + 10 y = 15.$

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Solution

The given equations are

$8 x + 5 y = 9$ ----(1)

$k x + 10 y = 15$ ----(2)

For no solution,

$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}} \Rightarrow \frac{8}{k} = \frac{5}{10} \neq \frac{9}{15} \Rightarrow \frac{8}{k} = \frac{5}{10} \Rightarrow k = 16$

Hence for no solution k should be 16

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For what value of k is the pair of equations $8 x + 5 y = 9 and kx + 10 y = 15$ inconsistent?

(a) $k = \frac{3}{5}$
(b) $k = \frac{5}{3}$
(c) k = 16
(d) k = −16

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Find the value of k for which each of the following systems of equations has no solution: 8x+5y=9,kx+10y=15.

The given equations are 8x+5y=9 ----(1) kx+10y=15 ----(2) For no solution, a1a2=b1b2≠c1c2⇒8k=510≠915⇒8k=510⇒k=16 Hence for no solution k should be 16

Find the value of k for which each of the following systems of equations has no solution:

$8 x + 5 y = 9, k x + 10 y = 15.$