Given the linear equation 2x + 3y − 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is :
(i) intersecting lines
(ii) parallel lines
(iii) coincident lines
(i) Given the linear equation are: $2 x+3 y-8=0$
We know that intersecting condition:
$\frac{a 1}{a 2} \neq \frac{b 1}{b 2}$
Where $a_{1}=2, b_{1}=3, c_{1}=-8$
Hence the equation of other line is $x+2 y-4=0$
(ii) We know that parallel line condition is: $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}$
Where $a_{1}=2, b_{1}=3, c_{1}=-8$
Hence the equation is $2 x+6 y-12=0$
(iii) We know that coincident line condition is: $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$
Where $a_{1}=2, b_{1}=3, c=-8$
Hence the equation is $4 x+6 y-16=0$