Question

find the value of a and b for which the following system of linear equations have infinitely many solution:3x-(a+1)y=2b-1 ; 5x +(1-2a)y=3b

Answer 1

Given pair of linear equations:
3x-(a+1)y=2b-1......................1
5x+(1-2a)y=3b......................2
Here we have,
a1=3 , a2=5 , b1=-a-1 , b2=1-2a , c1=2b-1 , c2=3b
The condition required for which pair of linear equation has infinitely many solution is,
a1/a2 = b1/b2 = c1/c2
By putting all values we have,
3/5 = (-a-1)/(1-2a) = (2b-1)/(3b)

3/5 = (-a-1)/(1-2a) and 3/5 = (2b-1)/(3b)

3-6a = -5a-5 and 9b =10b-5

a = 8 and b=5



For value of a=8 and b=5 ,the given pair of linear equation has infinitely many solutions.

Answer 2

Answer:

a=8 & b=5

Step-by-step explanation:

As,

A1=3, B1=-a-1, C1=2b-1

A2=5 B2=1-2a C2=3b

As, A1/A2=B1/B2=C1/C2

Part I

A1/A2=B1/B2

3/5 =-a-1/1-2a

5(-a-1) = 3(1-2a)

-5a-5=3-6a

-5 = 3-a

-8=-a

Cancelling the minus sign from both the sides

We get;

8=a

Part II

A1/A2=C1/C2

3/5=2b-1/3b

On cross multiplication

9b=10b-5

-b=-5

By cancelling minus sign from both the sides

We get,

b=5

Therefore , a=8 and b=5