Question

3x+2y=5 and 6x+4y=10 ifa1/a2 than these simultaneous equations have​

Answer 1

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

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

A pair of Straight Lines

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

have infinite number of solutions if $\displaystyle \: \: \frac{a_1}{a_2} = \frac{b_1}{b_2}=\frac{c_1}{c_2}$

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

Given pair of linear equations

$3x +2y = 5 \: \: and \: \: 6x + 4y =10$

Comparing with

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

We get

$\displaystyle \: a_1 = 3 \: , \: b_1 = 2 \: , c_1= 5 \: and \: \: a_2 = 6 \: , \: b_2 = 4\: , \: \: c_2= 10$

$\displaystyle \: \frac{a_1}{a_2} = \frac{3}{6} = \frac{1}{2}$

$\displaystyle \: \frac{b_1}{b_2} = \frac{2}{4} = \frac{1}{2}$

$\displaystyle \: \frac{c_1}{c_2} = \frac{5}{10} = \frac{1}{2}$

So $\displaystyle \: \: \frac{a_1}{a_2} = \frac{b_1}{b_2}=\frac{c_1}{c_2}$

Hence given system of equations have infinite number of solutions