Given the linear equation 2x + 3y - 8 = 0, write another linear equations in two variables such that the geometrical representation of the pair so formed is:
Given the linear equation 2x + 3y - 8 = 0, write another linear equations in two variables such that the geometrical representation of the pair so formed is:
(i) intersecting lines
(ii) parallel lines
(iii) coincident lines
(i) Intersecting lines:
For this condition,
a1/a2 ≠ b1/b2
The second line such that it is intersecting the given line is
2x + 4y - 6 = 0 as
a1/a2 = 2/2 = 1
b1/b2 = 3/4 and
a1/a2 ≠ b1/b2
(ii) Parallel lines
For this condition,
a1/a2 = b1/b2 ≠ c1/c2
Hence, the second line can be
4x + 6y - 8 = 0 as
a1/a2 = 2/4 = 1/2
b1/b2 = 3/6 = 1/2 and
c1/c2 = -8/-8 = 1
and a1/a2 = b1/b2 ≠ c1/c2
(iii) Coincident lines
For coincident lines,
a1/a2 = b1/b2 = c1/c2
Hence, the second line can be
6x + 9y - 24 = 0 as
a1/a2 = 2/6 = 1/3
b1/b2 = 3/9 = 1/3 and
c1/c2 = -8/-24 = 1/3
and a1/a2 = b1/b2 = c1/c2
