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:
(i) intersecting lines (ii) parallel lines (iii) coincident lines

Answer 1

a) Intersecting lines
Solution: For intersecting line, the linear equations should meet following condition:
$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$

For getting another equation to meet this criterion, multiply the coefficient of x with any number and multiply the coefficient of y with any other number. A possible equation can be as follows:
$4x+9y-8=0$

(b) Parallel lines
Solution: For parallel lines, the linear equations should meet following condition:
$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

For getting another equation to meet this criterion, multiply the coefficients of x and y with the same number and multiply the constant term with any other number. A possible equation can be as follows:
$4x+6y–24=0$

(c) Coincident lines
Solution: For getting coincident lines, the equations should meet following condition;
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

For getting another equation to meet this criterion, multiply the whole equation with any number. A possible equation can be as follows:
$4x+6y–16=0$