Question

Are the following pair of linear equations consistent?

$-3x-4y=12$,

$4y+3x=12$

• A. No
• B. Yes
• C. Data Insufficient
• D. None of these

Answer 1

The correct option is A No

The given pair of linear equations can be written as
$-3x-4y-12=0$ and $3x+4y-12=0$
Here $a_1=-3,b_1=-4,c_1=-12$
and $a_2=3,b_2=4,c_2=-12$
$\therefore \frac{a_1}{a_2}=\frac{-3}{3}=-1$
$\frac{b_1}{b_2}=\frac{-4}{4}=-1$
$\frac{c_1}{c_2}=\frac{-12}{-12}=1$
$\Rightarrow \frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
Hence the given pair of linear equations is inconsistent.