Question

The equations $2x + 3y + 4 = 0; 3x + 4y + 6 = 0$ and $4x + 5y + 8 = 0$ are

• A. consistent with unique solution
• B. inconsistent
• C. consistent with infinitely many solutions
• D. None of the above

Answer 1

Answer: (A)

Consider first two equations :
$2x + 3y = -4$ and $3x + 4y = -6$
We have $\Delta = \begin{vmatrix}2&3\\ 3&4\end{vmatrix} =-1 \ne0 $
$ \Delta_{x} = \begin{vmatrix}-4&3\\ -6&4\end{vmatrix} =2 $
and $ \Delta_{y} = \begin{vmatrix}2&-4\\ 3&-6\end{vmatrix} = 0 $
$\therefore \, x = -2 $ and $y = 0$
Now this solution satisfies the third, so the equations are consistent with unique solution.