Using determinants, find the area of the triangle with vertices $(-3, 5), (3, -6), (7, 2).$

If the points $\left(x, -2\right), \left(5, 2\right), \left(8, 8\right)$ are collinear, fing $x$ using determinants.

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

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