The population of Patna city is $96000$, the decreasing rate of population is $800$ per year. Population of Patliputra is $68000$, the increasing rate of population is $1200$ per year. In how many years will the population of both places be equal?

Determine whether the given system of equations is consistent or not.

$$\begin{gathered} \frac{3}{4}x+\frac{2}{4}y=20 \\ 10x+15y=35 \end{gathered}$$

Examine the consistency of the system of the following equation.

$2x-3y+5z=4$

$6x+4z=5$

$x+5y-7z=3$

Examine the following system of equations for consistency or inconsistency.
$$\begin{gathered} \frac{8}{3}x+6y-48=0 \\ 4x+9y-96=0 \end{gathered}$$

Examine the consistency of the system of equations.

$5x-y+4z=5$

$2x+3y+5z=2$

$5x-2y+6z=-1$

Determine whether the given system of equations is consistent or not.

$$\begin{gathered} 8\mathrm{x}+12\mathrm{y}-20=0, \\ 24\mathrm{x}+36\mathrm{y}-21=0 \end{gathered}$$