Question

for what value of k, the pair of linear equations 3x- ky+6 =0 and 2x+ 2y =0 does not have a solution ​

Answer 1

Answer:

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Step-by-step explanation:

Given :

3x -ky +6 =0

2x +2y =0

here

$a _{1} = 3 \: \: \: a_{2} = 2 \\ \: \: b_{1} = - k \: \: \: \: \: b_{2} = 2 \\ c_{1} = 6 \: \: \: \: c_{2} = 0$

for no solution the condition is

according to the Image

$\frac{ a_{1}}{ a_{2}} = \frac{ b_{1} }{ b_{2} } ≠\frac{ c_{1} }{ c_{2} }$

substitute the values in the condition we get

$\frac{3}{2} = \frac{ -k }{2} ≠\frac{6}{0} \\ \\ \frac{3}{2} = \frac{ -k }{2} \\ cross \: multiply \: we \: get \\ 6 = - 2k \\ - 2k \: = \: 6$

$k \: = \frac{6}{ - 2} \\ k \: = 3$

therefore the value of k is 3