Question

On comparing the ratios
(a1/a2), (b1/b2),(c1/c2)
and without
drawing them check, whether the system of
equations 9x + 8y – 15 = 0 and
15x+(40/3)y-25=0
intersect at a point, are parallel or coincide.

Answer 1

Given: Two lines: 9x + 8y – 15 = 0 and 15x + ( 40 / 3 ) y - 25 = 0

To find: Whether the lines are intersect at a point, are parallel or coincide.

Solution:

• Now the condition for intersecting lines is:

           a1 / a2 ≠ b1 / b2

• So comparing with given equations, we get:

          9 / 15 and 8 / 40/3

          9 / 15 and 24 / 40

          3 / 5 and 3 / 5

• So these are equal, so the lines are not intersecting.

• Now the condition for parallel lines is:

         a1 / a2 = b1 / b2 ≠ c1 / c2

• So comparing with given equations, we get:

         9 / 15 and 8 / 40/3 and -15 / -25

         9 / 15 and 24 / 40 and 3 / 5

         3 / 5 and 3 / 5 and 3 / 5

• So these all are equal, so the lines are not parallel.

• Now the condition for coincident lines is:

         a1 / a2 = b1 / b2 = c1 / c2

• So comparing with given equations, we get:

         9 / 15 and 8 / 40/3 and -15 / -25

         9 / 15 and 24 / 40 and 3 / 5

         3 / 5 and 3 / 5 and 3 / 5

• So these all are equal, so the lines are coincident lines.

Answer:

         So the given pair of lines is coincident lines.