Question

Express the following linear equations in the form $ax+by+c=0$ and indicate the values of $a,b$ and $c$ in each case:

(i) $2x+3y=9.3\overline{5}$
(ii) $x-\frac{y}{5}-10=0$
(iii) $-2x+3y=6$
(iv) $x=3y$
(v) $2x=-5y$
(vi) $3x+2=0$
(vii) $y-2=0$
(viii) $5=2x$

Answer 1

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

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

Comparing the equation with $ax+by+c=0$

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

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

Comparing the equation with $ax+by+c=0$

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

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

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

Comparing the equation with $ax+by+c=0$

$a=-2,b=3,c=-6$

(iv) $x=3y$

$\Rightarrow x-3y=0$

Comparing the equation with $ax+by+c=0$

$a=1,b=-3,c=0$

(v) $2x=-5y$

$\Rightarrow 2x+5y=0$

Comparing the equation with $ax+by+c=0$

$a=2,b=5,c=0$

(vi) $3x+2=0$

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

Comparing the equation with $ax+by+c=0$

$a=3,b=0,c=2$

(vii) $y-2=0$

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

Comparing the equation with $ax+by+c=0$

$a=0,b=1,c=-2$

(viii) $5=2x$

$\Rightarrow -2x+0y+5$

Comparing the equation with $ax+by+c=0$

$a=-2,b=0,c=5$