Question

2y − 3z = 0
x + 3y = − 4
3x + 4y = 3

Answer 1

These equations can be written as
0x + 2y − 3z = 0
x + 3y + 0z = − 4
3x + 4y + 0z = 3

$$\begin{gathered} D=\left|\begin{array}{ccc}0& 2& -3\\ 1& 3& 0\\ 3& 4& 0\end{array}\right| \\ =0(0-0)-2(0-0)-3(4-9) \\ =15 \\ {D}_1=\left|\begin{array}{ccc}0& 2& -3\\ -4& 3& 0\\ 3& 4& 0\end{array}\right| \\ =0(0-0)-2(0-0)-3(-16-9) \\ =75 \\ {D}_2=\left|\begin{array}{ccc}0& 0& -3\\ 1& -4& 0\\ 3& 3& 0\end{array}\right| \\ =0(0-0)-0(0-0)-3(3+12) \\ =-45 \\ {D}_3=\left|\begin{array}{ccc}0& 2& 0\\ 1& 3& -4\\ 3& 4& 3\end{array}\right| \\ =0(9+16)-2(3+12)-0(4-9) \\ =-30 \\ \mathrm{Now}, \\ x=\frac{D_1}{D}=\frac{75}{15}=5 \\ y=\frac{D_2}{D}=\frac{-45}{15}=-3 \\ z=\frac{D_3}{D}=\frac{-30}{15}=-2 \\ \therefore x=5,y=-3\mathrm{and}z=-2 \end{gathered}$$