If the points $\left(3, -2\right), \left(x, 2\right), \left(8, 8\right)$ are collinear, find $x$ using determinants. 

Using determinants, find the equation of the line joining the points

$(1, 2)$ and $(3, 6)$

Using determinants, find the equation of the line joining the points

$(3, 1)$ and $(9, 3)$

Find values of $k$ if area of triangle is $4$ square units whose vertices are

$(k, 0), (4, 0)$ and $(0, 2)$

Find values of $k$, if area of triangle is $4$ square units whose vertices are

$(-2, 0), (0, 4)$ and $(0, k)$

Solve the following systems of linear equations by Cramer's rule

$$\begin{gathered} x- 2y= 4 \\ -3x+ 5y= -7 \end{gathered}$$

Solve the following systems of linear equations by Cramer's rule

$\begin{array}{c}2x-y=1\\ 7x-2y=-7\end{array}$

Solve the following systems of linear equations by Cramer's rule

$\begin{array}{c}2x-y=17\\ 3x+5y=6\end{array}$

Solve the following systems of linear equations by Cramer's rule

$$\begin{gathered} 3x+y= 19 \\ 3x-y= 23 \end{gathered}$$