Question

find the value of a and b if equation have infinitely many solutions 3x+4y=12 (a+b)x+2(a-b)y=5a-1​

Answer 1

Answer:

a = 5 and b = 1

Step-by-step explanation:

A1/A2 = B1/B2 = C1/C2

this is condition 4 infinitely many solutions

2 lines r intersecting

A1 = 3 , A2 = a+b , B1 = 4 , B2 = 2(a-b) , C1 = 12 , C3 = 5a-1

A1/A2 = 3/a+b

B1/B2 = 4/2(a-b)

C1/C2 = 12/5a-1

Now equate A1/A2 and B1/B2

3/a+b = 4/2a-2b

now cross multiplication

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

6a-6b = 4a+4b

6a-4a = 6b+4b

2a =10b

a = 5b

now equate A1/A2 and C1/C2

3/a+b = 12/5a-1

now cross multiplication

3(5a-1) = 12(a+b)

15a-3 = 12a+12b

15a-12a = 12b+3

3a = 12b+3

now put value of 'a'

3(5b) = 12b+3

15b = 12b+3

15b-12b = 3

3b = 3

b = 1

now put the value of 'b' in 'a'

a = 5b

a = 5