Question

the pair of equations 3x + 5y = 3 and 9x + ky = 8 have no solution if k

Answer 1

$\huge\boxed{\underline{\underline{\green{Solution}}}} </p><p>$

$\displaystyle \: \longmapsto \: \:$FORMULA TO BE IMPLEMENTED :

A pair of Straight Lines

$\displaystyle \: a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0$

is said to have no solution if $\displaystyle \: \: \frac{a_1}{a_2} = \frac{b_1}{b_2}$

$\displaystyle \: \longmapsto \: \:$CALCULATION :

Given pair of linear equations

$3x +5y = 3 \: \: and \: \: 9x + ky =8$

Comparing with

$\displaystyle \: a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0$

We get

$\displaystyle \: a_1 = 3 \: , \: b_1 = 5 \: , c_1= - 3\: and \: \: a_2 = 9 \: , \: b_2 = k\: , \: \: c_2= - 8$

So

$\displaystyle \: \: \frac{a_1}{a_2} = \frac{b_1}{b_2} \: gives$

$\displaystyle \: \: \frac{3}{5} = \frac{9}{k}$

$\implies \: \displaystyle \: k = 15$

RESULT

Hence the required value of k is 15