Given the linear equation $3 x + 4 y + 11 = 0$ , write linear equations in two variables such that their geometrical representions form parallel lines and intersecting lines.

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Solution

(i) parallel lines
Equation of first line: $3 x + 4 y + 11 = 0$
Let the equation of second line be $a x + b y + c = 0$
For parallel lines-
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$
$\Rightarrow \frac{3}{a} = \frac{4}{b} \neq \frac{11}{c} . . . . . (1)$
Assuming any value of $a, b$ and $c$ such that equation $(1)$ is satified.
$3 x + 4 y + 22 = 0$
Hence the equation of second line be $3 x + 4 y + 22 = 0$ .
(ii) intersecting lines
Equation of first line: $3 x + 4 y + 11 = 0$
Let the equation of second line be $a x + b y + c = 0$
For intersecting lines-
$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
$\Rightarrow \frac{3}{a} \neq \frac{4}{b} . . . . . (2)$
Assuming any value of $a, b$ and $c$ such that equation $(2)$ is satified.
$6 x + 4 y + 11 = 0$
Hence the equation of second line be $6 x + 4 y + 11 = 0$ .

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Given the linear equation 3x+4y+11=0, write linear equations in two variables such that their geometrical representions form parallel lines and intersecting lines.

Given the linear equation $3 x + 4 y + 11 = 0$ , write linear equations in two variables such that their geometrical representions form parallel lines and intersecting lines.