Question

find the value of a and b for which the following pair of linear equation has infinite number of solutions 2x+3y=7, 2ax+(a+b)y=28

Answer 1

for infinite no. of solutions

a1/a2=b1/b2/c1/c2
therefore
2/2a=3/(a+b)=1/4
Now 3/a+b=1/4
therefore a+b=12
therefore b=12-a
now 1/a=1/4
therefore a=4
Now putting the value of a in eqn 1 we get,
b=12-4=8
Verification:-
now putting the value of a and b in equation given above:-
a1/a2=2/2 (4)=2/8=1/4
b1/b2=3/(4+8)=3/12=1/4
c1/c2=-7/-28=1/4
Now as a1/a2=b1/b2=c1/c2
therefore the equation will have infinite no. of solutions.

therefore a=4 and b=8
HOPE THIS ANSWER HELPS