Question

6.
Find the value of 'a' and 'b' the system has infinitely many solution
2x + 3y = 7
(a - b) x + (a + b) y = 3a + b-2.​

Answer 1

Answer:

a=5 and b=1

Step-by-step explanation:

If any two equation has infinitely many solutions then,

a1/a2 =b1/b2 = c1/c2. Given that those equations are in the form of a1x+b1y =c1 and a2x +b2y= c2.

So here ,

a1= 2 b1= 3 c1= 7

a2= a-b b2 = a+b c2 = 3a+b-2

so,

2/a-b = 3/a+b = 7 / 3a+b-2

now first taking the first equality.

2/a-b = 3/a+b

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

=> a = 5b ---------(1)

Now take any other equality.

3/a+b = 7/ 3a+b-2.

=> 9a+ 3b - 6 = 7a+ 7b.

=> 2a - 4b = 6

=> 10b -4b = 6 ( because a =5b

from equation no.1)

=> 6b = 6

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

Now put this value of b in equation no. 1

a =5b

=> a= 5.