Given the linear equation 2x + 3y − 8 = 0,


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) For intersecting lines,

Equation of another intersecting line to the given line is−

$2 x+5 y-3=0$


Since, condition for intersecting lines and unique solution is−

$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$

(ii) For parallel lines,


Equation of another parallel line to the given line is−

$2 x+3 y-3=0$

Since, condition for parallel lines and no solution is−

$\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

(iii) For co−incident lines,


Equation of another coincident line to the given line is−

$4 x+6 y-16=0$


Since, condition for coincident lines and infinite solution is−


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