Question

.
2x + 3y = 7
(a - b) x + (a + b) y = 3a + b - 2
$x - 3y - 3 = 0 3x - 2 = 0$
​

Answer 1

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