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

Two lines, a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0

If \(\frac{a_1}{a_2}\)=\(\frac{b_1}{b_2}\)=\(\frac{c_1}{c_2}\), then the lines coincide

If \(\frac{a_1}{a_2}\)= \(\frac{b_1}{b_2}\)≠\(\frac{c_1}{c_2}\), then the lines are parallel

If \(\frac{a_1}{a_2}\)≠ \(\frac{b_1}{b_2}\)≠\(\frac{c_1}{c_2}\), then the lines intersect

Given line 2x + 3y - 8 = 0

(i) intersecting line:

3x + 2y – 6 = 0

(ii) parallel line:

4x + 6y = 15

(iii) coincident line:

4x + 6y – 16 = 0