The system of simultaneous linear equations $x-2y+3z=4$,$3x+y-2z=7$,and $2x+3y+z=6$ has

Solve the system of equations $2x + 5y = 1$ and $3x + 2y = 7$.

Solve the system of linear equations using the matrix method: $x-y+z=4$,$2x+y-3z=0$,and $x+y+z=2$.

Let the system of linear equations $4x + \lambda y + 2z = 0$,$2x - y + z = 0$,and $\mu x + 2y + 3z = 0$ (where $\lambda, \mu \in R$) have a non-trivial solution. Then which of the following is true?

Let $S$ denote the set of all real values of $\lambda$ such that the system of equations $\lambda x + y + z = 1$,$x + \lambda y + z = 1$,and $x + y + \lambda z = 1$ is inconsistent. Then,$\sum_{\lambda \in S} (|\lambda|^2 + |\lambda|)$ is equal to

The number of $\theta \in (0, 4\pi)$ for which the system of linear equations $3(\sin 3\theta)x - y + z = 2$,$3(\cos 2\theta)x + 4y + 3z = 3$,and $6x + 7y + 7z = 9$ has no solution is: