Question

Find The value of k if it is a unique solution
kx+3y +7=0 and
15x+5y+4=0​

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 Unique Solution if $\displaystyle \: \: \frac{a_1}{a_2} \ne \frac{b_1}{b_2}$

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

Given pair of linear equations

$kx +3 y +7=0 \: \: and \: \: 15x+5y+4 =0$

Comparing with

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

We get

$\displaystyle \: a_1 = k \: , \: b_1 = 3</p><p> \: , c_1= 7\: and \: \: a_2 = 15 \: , \: b_2 = 5\: , \: \: c_2= 4$

So For unique Solution

$\displaystyle \: \: \frac{a_1}{a_2} \ne \frac{b_1}{b_2}$

$\displaystyle \: \implies \frac{k}{15} \ne \frac{3}{5}$

$\implies \: 5k \ne 45$

$\therefore \: k \: \ne 9$