Answer

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**Hint:**First, move all parts to the left side of the equation. Then, compare it with the equation $ax+by+c=0$. After that equate it with the coefficient of $x$, $y$ and constant part. The value of a, b and c is the desired result. We will follow the same approach for every part.

**Complete step by step answer:**

(i) Given: $2x+3y=9.3\overline{5}$

Move $9.3\overline{5}$ on the right side,

$\Rightarrow 2x+3y-9.3\overline{5}=0$

Compare the equation with $ax+by+c=0$,

$\Rightarrow a=2$

$\Rightarrow b=3$

$\Rightarrow c=9.3\overline{5}$

**Hence, the values are $a=2$, $b=3$ and $c=9.3\overline{5}$.**

(ii) Given: $x-\dfrac{y}{5}-10=0$

Compare the equation with $ax+by+c=0$,

$\Rightarrow a=1$

$\Rightarrow b=-\dfrac{1}{5}$

$\Rightarrow c=-10$

**Hence, the values are $a=1$, $b=-\dfrac{1}{5}$ and $c=-10$.**

(iii) Given: $-2x+3y=6$

Move 6 on the right side,

$\Rightarrow -2x+3y-6=0$

Compare the equation with $ax+by+c=0$,

$\Rightarrow a=-2$

$\Rightarrow b=3$

$\Rightarrow c=-6$

**Hence, the values are $a=-2$, $b=3$ and $c=-6$.**

(iv) Given: $x=3y$

Move 3y on the right side,

$\Rightarrow x-3y=0$

Compare the equation with $ax+by+c=0$,

$\Rightarrow a=1$

$\Rightarrow b=-3$

Since there is no constant part,

$\Rightarrow c=0$

**Hence, the values are $a=1$, $b=-3$ and $c=0$.**

(v) Given: $2x=-5y$

Move 5y on the right side,

$\Rightarrow 2x+5y=0$

Compare the equation with $ax+by+c=0$,

$\Rightarrow a=2$

$\Rightarrow b=5$

Since there is no constant part,

$\Rightarrow c=0$

**Hence, the values are $a=2$, $b=5$ and $c=0$.**

(vi) Given: $3x+2=0$

Compare the equation with $ax+by+c=0$,

$\Rightarrow a=3$

$\Rightarrow c=2$

Since there is no value of $y$,

$\Rightarrow b=0$

**Hence, the values are $a=3$, $b=0$ and $c=2$.**

(vii) Given: $y-2=0$

Compare the equation with $ax+by+c=0$,

$\Rightarrow b=1$

$\Rightarrow c=-2$

Since there is no value of x,

$\Rightarrow a=0$

**Hence, the values are $a=0$, $b=1$ and $c=-2$.**

(viii) Given: $5=2x$

Move 2x on the right side,

$\Rightarrow -2x+5=0$

Compare the equation with $ax+by+c=0$,

$\Rightarrow a=-2$

$\Rightarrow c=5$

Since there is no value of y,

$\Rightarrow b=0$

**Hence, the values are $a=-2$, $b=0$ and $c=5$.**

**Note:**

An equation is said to be a linear equation in two variables if it is written in the form of \[ax+by+c=0\], where a, b & c are real numbers and the coefficients of x and y, i.e. a and b respectively, are not equal to zero.

The solution for such an equation is a pair of values, one for x and one for y which further makes the two sides of an equation equal.

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