Question

Find the value of k which the system of equations kx-y=2, 6x-2y=0 has unique solutions.​

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

$kx - y = 2 \: \: and \: \: 6x - 2y =0$

Comparing with

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

We get

$\displaystyle \: a_1 = k \: , \: b_1 = - 1</p><p> \: , c_1= - 2\: and \: \: a_2 = 6 \: , \: b_2 = - 2\: , \: \: c_2= 0$

So For unique Solution

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

$\displaystyle \: \frac{k}{6} \ne \frac{1}{2}$

$\implies \: 2k \ne 6$

$\therefore \: k \: \ne 3$

Answer 2

Answer:

K IS NOT EQUAL TO 3..

Step-by-step explanation:

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