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

1.	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» 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 the linear equation 2x + 3y - 8 = 0. An intersecting line is x + 2y – 4 =0 A parallel line is 4x + 6y – 12 = 0 A coincident line is 4x + 6y – 16 = 0

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»

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 the linear equation 2x + 3y - 8 = 0.

An intersecting line is x + 2y – 4 =0

A parallel line is 4x + 6y – 12 = 0

A coincident line is 4x + 6y – 16 = 0