The system of linear equations $x + 2y + z = -3$,$3x + 3y - 2z = -1$,and $2x + 7y + 7z = -4$ has:

Consider the simultaneous linear equations $AX=B$ and $AY=Q$. If $A$ is an invertible matrix and $B$ is the unique solution of $AY=Q$, then the solution of $AX=B$ is

The set of equations $x - y + 3z = 2$,$2x - y + z = 4$,and $x - 2y + \alpha z = 3$ has:

Solve the system of linear equations using the matrix method: $2x - y = -2$ and $3x + 4y = 3$.

Consider the simultaneous linear equations $\beta x + \alpha y - z = -1$, $3x - \beta y + \alpha z = 0$, and $\alpha x + \beta y + z = 1$. In the usual notation used in Cramer's rule, given that $\frac{\Delta_1}{\Delta} = -1$, $\frac{\Delta_2}{\Delta} = 1$, and $\frac{\Delta_3}{\Delta} = 2$, then $(\alpha, \beta) = $

The number of solutions of the equations $x + y - z = 0$,$3x - y - z = 0$,and $x - 3y + z = 0$ is