Question

find the values of 'a' and 'b' if the pair of linear equations (a-4)x +2y+(2b+1)=0 and (a-1)d + 4y +(5b-1)=0 has infinite solutions​

Answer 1

Step-by-step explanation:

2x−(a−4)y=2b+1

4x−(a−1)y=5b−1

Considering 2x−(a−4)y=2b+1

Comparing with

a

1

x+b

1

y=c

1

a

1

=2

b

1

=−(−a−4)

and c

1

=2b+1

Now considering 4x−(a−1)y=5b−1

Comparing with

a

2

x+b

2

y=c

2

a

2

=4

b

2

=−(a−1)

and c

2

=5b−1

For infinite number of solutions ,

a

2

a

1

=

b

2

b

1

=

c

2

c

1

∴

4

2

=

−(a−1)

−(a−4)

=

5b−1

2b+1

Considering

a−1

a−4

=

2

1

⇒2a−8=a−1

⇒a=7

And now for b consider

5b−1

2b+1

=

2

1

⇒4b+2=5b−1

∴b=3

∴ The given system of equation will have infinitely many solution if a=7 and b=3.