Question

Find the value of a and b for which (9a-1)x +3y=2 and 6x+(1-2b)y =6 has infinitely many solutions.
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Answer 1

Answer.

(a-1)x+3y=2

(a-1)x+3y-2=0

since a1x+b1y+(-c1)=0

so here a1=(a-1),b1=3,c1=-2

now

6x+(1-2b)y=6

6x+(1-2b)y-6=0

since a2x+b2y+(-c2)=0

here a2=6,b2=(1-2b),c2=-6

Now for infinite solution we need

a1/a2=b1/b2=c1/c2

(a-1)/6=3/(1-2b)=-2/-6

first we will take b1/b2= c1/c2

i.e. 3/(1-2b)= 2/6

2(1-2b)=18

2-4b=18

-4b=18-2=16

b=-4

Now we will take

a1/a2=b1/b2

i.e.a-1/6=3/9. (b=-4)

=>3(a-1)=6. (3/9=1/3)

3a-3=6

3a=6+3

a=3

Answer 2

Sorry, couldn't fit the equation description.