Question

Which option of linear equation is inconsistent?

• A. $x+y=1$,$2x+y=0$
• B. $x-y=2$, $2x-2y=1$
• C. $2x-3y=0$, $2y+x=1$
• D. $2x-4y=19$, $-2x+y=0$

Answer 1

Answer: (B)

$x-y=2$,

$2x-2y=1$

The general form for a pair of linear equations in two variables $x$ and $y$ is

Option A:-
$x+y-1=0\Rightarrow a_1=1,b_1=1,c_1=-1$
$2x+y=0\Rightarrow a_2=2,b_2=1,c_2=0$
$\frac{a_1}{a_2}=\frac{1}{2}$
$\frac{b_1}{b_2}=\frac{1}{1}$
$\therefore \frac{a_1}{a_2}\ne \frac{b_1}{b_2}$
system of equations in option A is consistent
option B:-
$x-y=2$---(1)
$2x-2y=1$---(2)
Comparing equations (1) and (2) with the general form of equation to consider their co-efficient,
$a_1=1$, $a_2=2$,$b_1=-1$, $b_2=-2$, $c_1=2$, $c_2=1$
So, $\frac{1}{2}=\frac{-1}{-2}\ne \frac{2}{1}$
We know that $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$ is said to be inconsistent.
Hence, the equations are inconsistent.