Question

for what value of a and b will the pair of linear equations have infinitely many solutions x+2y=1 , (a-b)x+(a+b)y=a+b-2​

Answer 1

Step-by-step explanation:

For infinitely many solutions,

a

2

a

1

=

b

2

b

1

=

c

2

c

1

⇒

(a−b)

I

1

=

(a+b)

II

2



=

(a+b−2)

III

1

From ratio I and II

2a−2b=a+b

⇒a−3b=0

From ratio II and III

2a+2b−4=a+b

⇒a+b=4

a−3b=0

a+b=4

−4b=−4

⇒b=1

and a=4−b

⇒a=4−1

⇒a=3