For what value of $k$, the pair of equations $4x-3y=9$, $2x+ky=11$ has no solution.

Given: The pair of equations $4x-3y=9$, $2x+ky=11$ has no solution.

To do: To find the of $k$.

Solution: 

Given Equations:

$4x-3y=9$      ....................... $( 1)$

$2x+ky=11$      ....................... $( 2)$

Here $a_{1}=4,\ b_{1}=-3$ & $c_{1}=9$

$a_{2}=2,\ b_{2}=k$ & $c_{2}=11$

The pair of equation will have no solution if,

$\frac{a_1}{a_{2}}=\frac{b_{1}}{b_{2}}\
eq\frac{c_{1}}{c_{2}}$

$\Rightarrow \frac{1}{2}=\frac{-3}{k}\
eq\frac{9}{11}$

$\Rightarrow \frac{1}{2}=\frac{-3}{k}$

$\Rightarrow k=-6$

Thus for $k=-6$, given pair of equations will have no solution.



 

Updated on: 10-Oct-2022

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