The value of $k \in R$,for which the system of linear equations
$3x - y + 4z = 3$
$x + 2y - 3z = -2$
$6x + 5y + kz = -3$
has infinitely many solutions,is:

If $[x]$ is the greatest integer less than or equal to $x$ and $|x|$ is the modulus of $x$,then the system of three equations $\begin{aligned} & 2x + 3|y| + 5[z] = 0, \\ & x + |y| - 2[z] = 4, \\ & x + |y| + [z] = 1 \end{aligned}$ has

If the system of equations
$x+y+az=b$
$2x+5y+2z=6$
$x+2y+3z=3$
has infinitely many solutions,then $2a+3b$ is equal to $...........$.

Examine the consistency of the system of equations: $2x - y = 5$ and $x + y = 4$.

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:

If the system of linear equations: $x + y + z = 6, x + 2y + 5z = 10, 2x + 3y + \lambda z = \mu$ has infinitely many solutions,then the value of $\lambda + \mu$ equals: