Question

The pair of equations x - 2 y = -5 and 3x - 6y = 15 represent graphically
Parallel lines
Intersecting lines
Coinciding lines
None of these

Answer 1

Answer:

Parallel lines

Note:

★ If we consider two lines whose equations are ax + by + c = 0 and a'x + b'y + c' = 0 ;

Then ;

• They are intersecting if a/a' ≠ b/b'

• They are coincident if a/a' = b/b' = c/c'

• They are parallel if a/a' = b/b' = c/c'

Solution:

Here,

The given equations of lines are ;

x - 2y = -5

3x - 6y = 15

The given system of lines can be rewritten as ;

x - 2y + 5 = 0

3x - 6y - 15 = 0

Clearly,

a = 1

a' = 3

b = -2

b' = -6

c = 5

c' = -15

Thus,

a/a' = 1/3

b/b' = -2/-6 = 1/3

c/c' = 5/-15 = -1/3

Clearly,

a/a' = b/b' ≠ c/c'

Hence,

The given lines are parallel .