Examine the consistency of the system of following equations. 

$\begin{array}{l}3x+4y=1\\ 2x+y=4\end{array}$

On comparing the ratios $\frac{a_1}{a_2}$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, and without drawing them, find out whether the lines representing the following pairs of linear equations are consistent or not.

$ax+by=c$

$lx+my=n$

Examine the consistency of the system of equations.

$x+2y=2$

$2 x+3y=3$

Examine the following system of equations for consistency or inconsistency

.$\mathrm{x}-\mathrm{y}+3\mathrm{z}=6, \mathrm{x}+3\mathrm{y}-3\mathrm{z}=-4, 5\mathrm{x}+3\mathrm{y}+3\mathrm{z}=10$

Examine the following system of equations for consistency or inconsistency.
$$\begin{gathered} 3x+y+4=0 \\ 6x+2y+8=0 \end{gathered}$$

Examine the following system of equations for consistency or inconsistency.

$\mathrm{x}-2\mathrm{y}+3\mathrm{z}=6, \mathrm{x}+4\mathrm{y}+\mathrm{z}=12, \mathrm{x}-3\mathrm{y}+2\mathrm{z}=1$