Question

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

Find the value of a and b

the following system of linear equations has an infinite no.
of solutions.

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Answer 1

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