Question

Find the values of a & b for which of the following system of linear equation has infinitely many solution 2x +3y =7( a+ b)x+(2a- b) y =3(a+b+1)​

Answer 1

Answer:

Given lines

2x - 3y = 7

(a+b)x-(a+b-3)y = 4a+b

for infinite solution of two given

lines a_{1}x+b_{1}y+c_{1}=0 : a_{2}x+b_{2}y+c_{2} = 0$$

a

2

a

1

=

b

2

b

1

=

c

2

c

1

a+b

2

=

a+b−3

3

=

4a+b

7

2a+2b-6 = 3a+3b 12a+3b = 7a + 7b -21

a+b = -6 5a - 4b = -21 --(2)

4c + 4b = -24 --(1)

(1)+(2) ⇒ 90 = -45 ⇒ a = -5

−5+b=−6=1b=−6+5=−1

a = -5, b = -1