Question

2x-3y=7
(a+b)x-(a+b-3)y=4a+b

Answer 1

a1/a2=b1/b2=c1/c2

2/(a+b)=-3/(-a-b+3)=7/4a+b

2/a+b=7/4a+b

8a+2b=7a+7b

1a-5b=0.....1

-3/-a-b+3=7/4a+b

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

-5a+4b=21....2

1*-5

-5a+25b=0

1-2

-5a+25b=0

-5a+4b=21

21b=-21

b=-1

substituting the value of b in 2

therefore a=5

therefore a and b satisfies equation a+5b=0

5-5=0

Answer 2

condition for infinite solution :

a1/a2= b1/b2=c1/c2

2/(a+b)= -3/-(a+b-3)=7/(4a+b)

2/(a+b)= 7/4a+b

8a+2b=7a+7b

a=5b.........(i)

-3/-(a+b-3)=7/(4a+b=)

3(4a+b)=7(a+b-3)

12a+3b=7a+7b-21.........(ii)

12(5b)+3b=7(5b)+7b-21.

substitute (i) in(ii)

(60+3)b=35b+7b-21

21=(-63+42)b

21=-21b

b=-1

a=5 (-1)

a=-5 , b=-1