Question

State whether the pair of linear equations 2x + 3y = 7 and 4x – 6y = 14 is consistent or inconsistent ?

Answer 1

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Answer 2

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

$\displaystyle \: \longmapsto \: \:$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 be consistent if $\displaystyle \: \: \frac{a_1}{a_2} \ne \frac{b_1}{b_2}$

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

Given pair of linear equations

$2x +3y = 7 \: \: and \: \: 4x - 6y =14$

Comparing with

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

We get

$\displaystyle \: a_1 = 2 \: , \: b_1 = 3</p><p>\: , c_1= 7 \: and \: \: a_2 = 4 \: , \: b_2 = - 6\: , \: \: c_2= 14$

$\displaystyle \: \frac{a_1}{a_2} = \frac{2}{4} = \frac{1}{2}$

And

$\displaystyle \: \frac{b_1}{b_2} = \frac{3}{ - 6} = - \frac{1}{2}$

Hence

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

Hence given pair of lines are consistent