Question

4. Find the values of a and b for which the following system of equations has
infinitely many solutions:
i. 3x+4y =12
(a+b)x +2(a-b)y=5a-1
ii. 2x+3y-9=0
(a+ b)x + (2a -b) y =3(a+b+1)
iii. 2x + 3y = 7
(a-1)x + (a+2) y = 3a

Answer 1

Step-by-step explanation:

i. Given equations

3x+4y=12

(a+b)x+2(a-b)y=5a-1

Condition for infinitely many solution

3/(a+b)=4/2(a-b)=12/(5a-1)

Now 3*2(a-b)=(a+b)4

3a-3b=2a+2b. (cancelling 2 from both side)

a=5b. (1)

Now 4/2(a-b)=12/(5a-1)

2/(a-b)=12/(5a-1)

2/(5b-b)=12/(25b-1). (substituting a=5b)

2/4b=12/25b-1

50b-2=48b

b=1

Now a=5b=5