Question

Which of the following pairs of linear equations is inconsistent?
$1.x+3y–5=0,2x+y=0$
$2.2x+y=1,2y=2–4x$
$3.2x–y=2,2y–4x=2$

• A. $x+3y–5=0,2x+y=0$
• B. $2x+y=1,2y=2–4x$
• C. $2x–y=2,2y–4x=2$
• D. All of the above.

Answer 1

The correct option is C

$2x–y=2,2y–4x=2$

$1.x+3y–5=0,2x+y=0$

$\Rightarrow \frac{1}{2}\ne \frac{3}{1}$, The pair of linear equations is consistent.

$2.2x+y=1,2y=2–4x$

$\Rightarrow \frac{2}{4}=\frac{1}{2}=\frac{1}{2}$, The pair of linear equations is consistent.

$3.2x–y=2,2y–4x=2$

$\Rightarrow \frac{-2}{4}=\frac{-1}{2}\ne \frac{2}{2}$, The pair of linear equations is inconsistent.