Question

find a and b for which the following system of linear equation has infinite number of solutions​

Answer 1

Answer:

a = 7

b = 3

Step-by-step explanation:

Given a pair of linear equations such that,

2x - (a-4)y = 2b + 1 .......(1)

4x - (a-1)y = 5b - 1 ........(2)

Also, given that,

They have infinite number of solutions.

To find the value of a and b.

We know that,

For infinite solutions,

• a1/a2 = b1/b2 = c1/c2

Substituting the values, we get,

=> 2/4 = -(a-4)/-(a-1) = (2b+1)/(5b-1)

=> 1/2 = (a-4)/(a-1) = (2b+1)/(5b-1)

Here, we have,

=> (a-4)/(a-1) = 1/2

=> 2(a-4) = a-1

=> 2a - 8 = a - 1

=> 2a - a = 8-1

=> a = 7

And

=> (2b+1)/(5b-1) = 1/2

=> 2(2b+1) = 5b-1

=> 4b + 2 = 5b - 1

=> 5b-4b = 2+1

=> b = 3

Hence, required values of a = 7 and b = 3.