Question

if the systems of equation 2x +3y= 7and (a+b) x+(2a-b)y=21 has iinfinitely many solutions than​

Answer 1

Answer:

see the answer in the attachment please

Answer 2

2x+3y=7

(a+b)x+(2a−b)y=21

Condition for infinitely many solutions is

a

2

a

1

=

b

2

b

1

=

c

2

c

1

⇒

a+b

2

=

2a−b

3

=

21

7

when

a+b

2

=

3

1

⇒a+b=6 .........(i)

when

2a−b

3

=

3

1

⇒2a−b=9 ...........(ii)

Adding eq (i) and (ii)

3a=15

we get a=5 and

5+b=6

b=1.