The following system of equations $3x - 7y + 5z = 3$,$3x + y + 5z = 7$,and $2x + 3y + 5z = 5$ is:

The system of equations $x+y+z=6$,$x+2y+5z=9$,$x+5y+\lambda z=\mu$ has no solution if

The number of values of $\alpha$ for which the system of equations: $x+y+z=\alpha$,$\alpha x+2 \alpha y+3 z=-1$,and $x+3 \alpha y+5 z=4$ is inconsistent,is:

If the system of linear equations $x + ay + z = 3$,$x + 2y + 2z = 6$,and $x + 5y + 3z = b$ has no solution,then:

If the system of equations $x+2y-3z=2$,$2x+\lambda y+5z=5$,$14x+3y+\mu z=33$ has infinitely many solutions,then $\lambda+\mu$ is equal to:

Let $S_1$ and $S_2$ be respectively the sets of all $a \in R - \{0\}$ for which the system of linear equations
$a x + 2 a y - 3 a z = 1$
$(2 a + 1) x + (2 a + 3) y + (a + 1) z = 2$
$(3 a + 5) x + (a + 5) y + (a + 2) z = 3$
has a unique solution and infinitely many solutions,respectively. Then: