The following system of linear equations $7x + 6y - 2z = 0$; $3x + 4y + 2z = 0$; $x - 2y - 6z = 0$ has:

If ${x^a}{y^b} = {e^m}$,${x^c}{y^d} = {e^n}$,${\Delta _1} = \left| {\begin{array}{*{20}{c}} m & b \\ n & d \end{array}} \right|$,${\Delta _2} = \left| {\begin{array}{*{20}{c}} a & m \\ c & n \end{array}} \right|$,and ${\Delta _3} = \left| {\begin{array}{*{20}{c}} a & b \\ c & d \end{array}} \right|$,then the values of $x$ and $y$ are respectively:

The solution of equations $x + y = 10$,$2x + y = 18$,and $4x - 3y = 26$ is:

The number of non-trivial solutions of the system $x-y+z=0, x+2y-z=0, 2x+y+3z=0$ is

If $\begin{bmatrix} 1 & 1 & 1 \\ 1 & -2 & -2 \\ 1 & 3 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 0 \\ 3 \\ 4 \end{bmatrix}$,then $\begin{bmatrix} x \\ y \\ z \end{bmatrix}$ is equal to

Solve the system of linear equations using the matrix method: $4x - 3y = 3$ and $3x - 5y = 7$.