Question

find the value of a and b for which the given pair of linear has infinitely many solution 5x-(a+1)y=3b-1 7x+(1-2a)y=4b​

Answer 1

Answer:

a=8 &b=5

Step-by-step explanation:

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

Answer 2

Answer:

3x−(a−1)y=2b−1-------(1)

5x+(1−2a)y=3b--------(2)

Here a1=3,b1=−(a+1) and c1=2b−1

Or a2=5,b2=(1−2a) and c2=3b

Give the system of equations have infinite solutions

$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2} \\ \frac{3}{5} = \frac{ - (a + 1)}{(1 - 2a)}$

⇒−5(a+1)=3(1−2a)

⇒−5a−5=3−6a

⇒a=8

$\frac{3}{5} = \frac{2b - 1}{3b}$

⇒9b=10b−5

⇒b=5