Question

find the value of a and b for which the system of equations 2x -(2a+5)y=5 -(2b+1)x-9y =15 has infinetly many solutions

Answer 1

Hey Mate! Here Is Your Answer

Step-by-step explanation:

Solution :-

For infinite solution in case of any two equations

ax + by + c = 0 and Ax + By + C = 0

When a/A = b/B = c/C

∴ 2/(2b + 1) = -(2a + 5)/-9 = 5/15

2/(2b + 1) = 5/15 = 1/3

⇒ 6 = 2b + 1 ⇒5 = 2b

⇒b = 5/2

(2a + 5)/9 = 5/15 = 1/3

⇒(2a + 5)/3 = 1

⇒2a + 5 = 3

⇒2a = -2 ⇒a = -1

Hence , a = -1 and b = 5/2

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