Solution

Let the cost of a notebook and a pen be $x$ and $y$ respectively.

Cost of notebook $=2 \times$ Cost of pen $x=2 y x-2 y=0$

Solution

$ \begin{aligned} & \text { (i) } 2 x+3 y=9.3 \overline{5} \\ & \Rightarrow 2 x+3 y-9.3 \overline{5} \end{aligned} $

Comparing the equation with $\mathrm{ax}+\mathrm{by}+\mathrm{c}=0$

$ a=2, b=3, c=-9.3 \overline{5} $

(ii) $x-\frac{y}{5}-10=0$

Comparing the equation with $a x+b y+c=0$

$ \mathrm{a}=1, \mathrm{~b}=-\frac{1}{5}, \mathrm{c}=-10 $

$ \begin{aligned} & \text { (iii) }-2 \mathrm{x}+3 \mathrm{y}=6 \\ & \Rightarrow-2 \mathrm{x}+3 \mathrm{y}-6=0 \end{aligned} $

Comparing the equation with $a x+b y+c=0$

$ \mathrm{a}=-2, \mathrm{~b}=3, \mathrm{c}=-6 $

(iv) $x=3 y$

$ \Rightarrow \mathrm{x}-3 \mathrm{y}=0 $

Comparing the equation with $\mathrm{ax}+\mathrm{by}+\mathrm{c}=0$

$ \mathrm{a}=1, \mathrm{~b}=-3, \mathrm{c}=0 $

(v) $2 \mathrm{x}=-5 \mathrm{y}$

$ \Rightarrow 2 \mathrm{x}+5 \mathrm{y}=0 $

Comparing the equation with $\mathrm{ax}+\mathrm{by}+\mathrm{c}=0$

$ \mathrm{a}=2, \mathrm{~b}=5, \mathrm{c}=0 $

$ \begin{aligned} & \text { (vi) } 3 x+2=0 \\ & \Rightarrow 3 x+0 y+2=0 \end{aligned} $

Comparing the equation with $\mathrm{ax}+\mathrm{by}+\mathrm{c}=0$

$ \mathrm{a}=3, \mathrm{~b}=0, \mathrm{c}=2 $

(vii) $y-2=0$

$ \Rightarrow 0 \mathrm{x}+\mathrm{y}-2=0 $

Comparing the equation with $a x+b y+c=0$

$ \mathrm{a}=0, \mathrm{~b}=1, \mathrm{c}=-2 $

(viii) $5=2 \mathrm{X}$

$ \Rightarrow-2 \mathrm{x}+0 \mathrm{y}+5 $

Comparing the equation with $\mathrm{ax}+\mathrm{by}+\mathrm{c}=0$

$ \mathrm{a}=-2, \mathrm{~b}=0, \mathrm{c}=5 $