Question

why does the hot chimney of a hurricane burst when cold water is poured on it​

Answer 1

2x-3y=7,(a+b+1)x+(a+2b+2)y=4(a+b)+1.​

we need to find values of a & b so that these equations have infinite solutions

2/(a+b+1)  =  -3/(a+2b +2)  = 7/(4(a+b) + 1)

Equating 1st & 2nd

=> 2a + 4b + 4 = -3a -3b - 3

=> 5a + 7b = - 7   eq 1

Equating 1st & 3rd

8a + 8b + 2  = 7a + 7b + 7

=> a + b  = 5     eq 2

eq 1  - 5Eq2

=> 2b = -32

=> b = -16

putting in eq 2

a = 21

a = 21 & b = -16 will give infinite solution

with these values

(a+b+1)x+(a+2b+2)y=4(a+b)+1  becomes

6x - 9y = 21

Diving by 3

2x - 3y = 7