Mathematics - Determinant Question with Solution | TestHub

Consider first two equations: $2x+3y=-4$ and $3x+4y=-6$ We have $\Delta =\left|\begin{array}{ll}2& 3\\ 3& 4\end{array}\right|=-1\ne 0$ $${\Delta }_{\mathrm{x}}=\left|\begin{array}{ll}-4& 3\\ -6& 4\end{array}\right|=2\text{ and }{\Delta }_{\mathrm{y}}=\left|\begin{array}{cc}2& -4\\ 3& -6\end{array}\right|=0$$ $\therefore x=-2$ and $y=0$ Now this solution satisfies the third, so the equations are consistent with unique solution.