Which of the following equations have a unique solution or infinitely many solutions. (i) x−3y−3=0;3x−9y−2=0 (ii) 2x+y=5;3x+2y=8

In the following equations we need to find which one have a unique solution or infinitely many solutions.

(i) x−3y−3=0; 3x−9y−2=0

comparing the given equations, with pair of general equations;

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

a1/a2 = 1/3, b1/b2 = -3/-9 = 1/3, c1/c2 = 3/2

a1/a2 = b1/b2 ≠ c1/c2

Thus, the pair of equations has no solutions.

(ii) 2x+y=5; 3x+2y=8

comparing the given equations, with pair of general equations;

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

a1/a2 = 2/3

b1/b2 = 1/2

c1/c2 = 5/8

a1/a2 ≠ b1/b2 ≠ c1/c2

Thus, the given lines have unique solution

Was this answer helpful?

 
   

0 (0)

(0)
(0)

Choose An Option That Best Describes Your Problem

Thank you. Your Feedback will Help us Serve you better.

Leave a Comment

Your Mobile number and Email id will not be published. Required fields are marked *

*

*

BOOK

Free Class

Ask
Question