Write whether the following statements are True or False? Justify your answers.

$(i)$ $a x+b y+c=0,$ where $a, b$ and $c$ are real numbers, is a linear equation in two variables.

$(ii)$ A linear equation $2 x+3 y=5$ has a unique solution.

$(iii)$ All the points $(2,0),(-3,0),(4,2)$ and $(0,5)$ lie on the $x$ -axis.

Solve the equation $2 y+1=y+4$ and represent the solution(s) on $(1)$ the number line $(2)$ the Cartesian plane.

Write four solutions for each of the following equations

$2 x-12=0$

Examine which of the following points are solutions of the equation $3 x-2 y=12,$ and which are not

$(1)(0,-6)$

$(2)(2,3)$

$(3)(2,-3)$

$(4)(-4,0)$

$(5)(-2,-9)$

$(6)(6,4)$

If the graph of equation $3 x+a y=7$ passes through the point $(3,-1),$ then the value of $a=\ldots \ldots \ldots$