Given the linear equation 2x + 3y - 8 = 0, write another linear e… - Vidyadip

Question

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:

intersecting lines
parallel lines
coincident lines

✓

Answer

Given, linear equation is $2x + 3y - 8 = 0 ...(i)$
Given: $2x + 3y - 8 = 0 ..... (i)$

For intersecting lines, $\frac { a _ { 1 } } { a _ { 2 } } \neq \frac { b _ { 1 } } { b _ { 2 } }$
$\therefore$ Any line intersecting with eq $(i)$ may be taken as $3x + 2y - 9 = 0$
or $3x + 2y - 7 = 0$
For parallel lines, $\frac { a _ { 1 } } { a _ { 2 } } = \frac { b _ { 1 } } { b _ { 2 } } \neq \frac { c _ { 1 } } { c_ { 2 } }$
$\therefore$ Any line parallel with eq$(i)$ may be taken as $6x + 9y + 7 = 0$
or $2x +3y - 2 = 0$
For coincident lines, $\frac { a _ { 1 } } { a _ { 2 } } = \frac { b _ { 1 } } { b _ { 2 } } = \frac { c _ { 1 } } { c_ { 2 } }$
$\therefore$ Any line coincident with eq $(i)$ may be taken as $4x + 6y - 16 = 0$
or $6x + 9y - 24 = 0$

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