Check the given systems of equations to see if it has a unique solution, infinitely many solutions or no solution. Solve them graphically.

$$\begin{gathered} 3x+2y=6 \\ 6x+4y=18 \end{gathered}$$

Find the value of $\text{'}k\text{'}$ for which the pair of equations $2x-ky+3=0, 4x+6y-5=0$ represent parallel lines.

For what value of $k,$ the pair of equations $3x+4y+2=0$ and $9x+12y+k=0$ represents coincident lines.

For what positive value of $\text{'}p\text{'},$ the following pair of linear equations have infinitely many solutions?

$px+3y-\left(p-3\right)=0$

$12x+py-p=0$

By comparing the ratios $\frac{a_1}{a_2}, \frac{b_1}{b_2}, \frac{c_1}{c_2}$, state whether the lines represented by the following pairs of linear equations intersect at a point, are parallel or are coincident.

$5x-4y+8=0$

$7x+6y-9=0$

By comparing the ratios $\frac{a_1}{a_2}, \frac{b_1}{b_2}, \frac{c_1}{c_2}$, state whether the lines represented by the following pairs of linear equations intersect at a point, are parallel or are coincident.

$9x+3y+12=0$

$18x+6y+24=0$

By comparing the ratios $\frac{a_1}{a_2}, \frac{b_1}{b_2}, \frac{c_1}{c_2}$, state whether the lines represented by the following pairs of linear equations intersect at a point, are parallel or are coincident.

$6x-3y+10=0$

$2x-y+9=0$

Check whether the following equations are consistent or inconsistent. Solve them graphically.

$3x+2y=5$

$2x-3y=7$