Question

determine the value of a and b for which the system of equations has infinitely many solutions : 2x+3y=7 and (a-b) X+(a+b) y = 3a+b-1​

Answer 1

Answer:

2x+3y=7

(a−b)x+(a+b)y=3a+b−2

∵ It has infinitely many solutions.

∴

a

2

a

1

=

b

2

b

1

=

c

2

c

1

(i)

a−b

2

=

(ii)

a+b

3

=

(iii)

3a+b−2

7

From (i) and (ii)

a+b

3

=

3a+b−2

7

7a+7b=9a+3b−6

⇒2a−4b=6

⇒a−2b=3

⇒5b−2b=3

⇒3b=3⇒b=1

∴a=5×1=5.