Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Solving the $3{\mathrm{eq}}^n$ s will give as the required point of intersection $\begin{array}{rl}& x-2y+4z=-4\\ & x+y+z=8\\ & x-y+2z=-1\\ & D=\left|\begin{array}{ccc}1& -2& 4\\ 1& 1& 1\\ 1& -1& 2\end{array}\right|=1(3)+2(1)+4(-2)=-3\\ & \begin{array}{rl}{D}_1=\left|\begin{array}{rrr}-4& -2& 4\\ 8& 1& 1\\ -1& -1& 2\end{array}\right|=& -4(3)+2(17)+4(-7)\\ & =-6\end{array}\\ & D_2=\left|\begin{array}{ccc}1& -4& 4\\ 1& 8& 1\\ 1& -1& 2\end{array}\right|=-15\\ & D_3=\left|\begin{array}{ccc}1& -2& -4\\ 1& 1& 8\\ 1& -1& -1\end{array}\right|=-3\\ & x=\frac{D_1}{D}=2,y=\frac{D_2}{D}=5,z=\frac{D_3}{D}=1\\ & \end{array}$ $(2,S,1)$ is the required point.