Question

We have a linear equation :
2x + 3t - 8 = 0 . Write another linear equation in two variable x and y such that the geometrical representation of the pair so formed is intersecting lines .
Now , write two more linear equation s o that two more linear equation so that one forms a pair of parallel lines and the second forms councident line with the given equation .

Answer 1

2x + 3y - 8 = 0
The lines intersecting lines .
Let the other linear equation be
ax + by + c = 0
$\therefore \frac{a_1}{a_2}\ne \frac{b_1}{b_2}$
We choose appripriciate values of satisfy the condition above .$\therefore$ The other equation may be 3x + 5y - 6 = 0
Parallel line$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c1}{c_2}$
2x + 3y - 8 = 04x = 6y - 10 =0
coinsistent lines $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
$2x+3y-8=0\Rightarrow 8x+12y-32=0$