Question

2x-(2a+5)y=5,(2b+1)x-9y=15 find a&b

Answer 1

Your question is incomplete .
A complete question is --------> find a and b when equations have infinity solutions .

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

Answer 2

Step-by-step explanation:

the complete question is

find the values of a and b for which the following system of equations has infinitely many solutions

2x-(2a+5)y = 5

(2b+1)x-9y = 15

Answer

the given system of equations is

2x-(2a+5)y = 5

(2b+1)x-9y = 15

=> 2x-(2a+5)y-5 = 0

(2b+1)x-9y-15 = 0

here,

a1=2

b1=2a+5

c1=(-5)

a2=2b+5

b2=9

c2=(-15)

for having infinitely many solutions,

we must have,

a1/a2 = b1/b2 = c1/c2

=> 2/2b+1 = 2a+5/9 = -5/-15

=> 2/2b+1 = 2a+5/9 = 5/15

first and last give,

=> 2/2b+1 = 5/15 = 1/3

=> 6=2b+1

=> 5=2b

=> b=5/2

second and last give,

=> 2a+5/9 = 5/15 = 1/3

=> 2a+5/3 = 1

=> 2a+5 = 3

=> 2a = -2

=> a = -2/2=(-1)

hence, for having infinitely many solutions, a = -1 and b = 5/2