Question

If the pair of linear equations 3x-5y=11 and (5a+b)x-(7a-b)y=4(3a-2b)+1 have infinitely many solutions,then find the values of a and b .

Answer 1

The pair of linear equations 3x - 5y = 11 and (5a + b)x - (7a - b)y = 4(3a - 2b) + 1, have infinitely many solutions.

To find : The values of a and b.

solution :

concept : system of two linear equations a₁x + b₁y = c₁ and a₂x + b₂y = c₂ have infinitely many solutions only if a₁/a₂ = b₁/b₂ = c₁/c₂

using above concept we get,

3/(5a + b) = -5/-(7a - b) = 11/{4(3a - 2b) + 1}

⇒3/(5a + b) = 5/(7a - b)

⇒3(7a - b) = 5(5a + b)

⇒21a - 3b = 25a + 5b

⇒4a + 8b = 0

⇒a + 2b = 0 ........(1)

3/(5a + b) = 11/{4(3a - 2b) + 1}

⇒3{4(3a - 2b) + 1} = 11(5a + b)

⇒12(3a - 2b) + 3 = 55a + 11b

⇒36a - 24b + 3 = 55a + 11b

⇒19a + 35b = 3 .......(2)

from equations (1) and (2) we get,

b = -1, a = 2

Therefore the values of a = 2 and b = -1

Answer 2

Answer:

a = -2

b = -1

Step-by-step explanation: