Using Cramer's rule, solve the following system of linear equations:

$\frac{2}{x}+\frac{3}{y}=2$

$\frac{5}{x}+\frac{8}{y}=\frac{31}{6}$.

Using Cramer's rule, solve the following system of linear equations:

$3x+ay=4$

$2x+ay=2, a\ne 0$.

Using Cramer's rule, solve the following system of linear equations:

$5x-7y+z=11$

$6x-8y-z=15$

$3x+2y-6z=7$.

Using Cramer's rule, solve the following system of linear equations:

$x+y+z+1=0$

$x+2y+3z+4=0$

$x+3y+4z+6=0$.

Using Cramer's rule, solve the following system of linear equations:

$4x-2y+9z+2=0$

$3x+4y+z-5=0$

$x-3y+2z-8=0$.

Using Cramer's rule, solve the following system of linear equations:

$x+y=2$

$2x-z=1$

$2y-3z=1$.

Using Cramer's rule, solve the following system of linear equations:

$2x-3y=1$

$x+3z=11$

$x+2y+z=7$.

Using Cramer's rule, solve the following system of linear equations:

$\frac{2}{x}+\frac{3}{y}+\frac{10}{z}=4$

$\frac{4}{x}-\frac{6}{y}+\frac{5}{z}=1$

$\frac{6}{x}+\frac{9}{y}-\frac{20}{z}=2$.

Using Cramer's rule, solve the following system of linear equations:

$x+y+z=1$

$ax+by+cz=k$

$a^{2}x+b^{2}y+c^{2}z=k^2$ where $a, b, c$ are all different.