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 $\Delta =\left|\begin{array}{cc}2& 3\\ 3& 4\end{array}\right|=-1\ne 0$
${\Delta }_x=\left|\begin{array}{cc}-4& 3\\ -6& 4\end{array}\right|=2$
and ${\Delta }_y=\left|\begin{array}{cc}2& -4\\ 3& -6\end{array}\right|=0$
$\therefore x=-2$ and $y=0$
Now this solution satisfies the third, so the equations are consistent with unique solution.