Question

For what value of a and b would the following pair of linear equations have infinite solutions
2x - 3y = 7, (a + b)x - (a - b - 3)y = 21

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Answer 1

Answer:

Hello mate..

Step-by-step explanation:

The equations are

2x−3y−7=0

(a+b)x−(a+b−3)y−(4a+b)=0

Here, a

1

=2,b

1

=−3,c

1

=−7

a

2

=a+b,b

2

=−(a+b−3),c

2

=−(4a+b)

The system of linear equations has infinite solutions

∴

a

2

a

1

=

b

2

b

1

=

c

2

c

1

⇒

a+b

2

=

−(a+b−3)

−3

=

−(4a+b)

−7

⇒

a+b

2

=

(a+b−3)

3

⇒2a+2b−6=3a+3b

⇒b=−a−6

Again, we have

⇒

(a+b−3)

3

=

(4a+b)

7

⇒12a+3b=7a+7b−21

⇒5a−4b=−21

Putting b=−a−6

⇒5a−4(−a−6)=−21⇒9a=−45

⇒a=−5

Putting a=−5inb=−a−6

⇒b=−(−5)−6⇒b=−1

⇒a=−5,b=−1

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Answer 2

Step-by-step explanation:

a=9 and b=-3

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