Question

If system of equations
$cx+y+1=0$
$x+cy+2=0$
$x+y+1=0$
is consistent then the values of $c$ is equal to

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

Answer: (A)

$2$

$D=\left|\begin{array}{ccc}c& 1& 1\\ 1& c& 2\\ 1& 1& 1\end{array}\right|=0$
$\Rightarrow c^2-3c+2=0\Rightarrow c=1,2$
for $c=1$ system become
$x+y+1=0$
$x+y+2=0$
$x+y+1=0$
which is inconsistent system
Now for $c=2$
$2x+y+1=0$
$x+2y+1=0$
$x+y+1=0$
which are concurrent lines $\Rightarrow$ $c=2$