Infinite number of solutions! Find a and b.
(2a-1)x-3y=5;3x+(b-2)y=3;

As the equations have infinite number of solutions, a1/a2=b1/b2=c1/c2.

Here, (2a-1)/3=-3/(b-2)=5/3.
How to proceed. I am stuck at the cross multiplying and finding out both a and b.

Question

Infinite number of solutions! Find a and b.
(2a-1)x-3y=5;3x+(b-2)y=3;

As the equations have infinite number of solutions, a1/a2=b1/b2=c1/c2.

Here, (2a-1)/3=-3/(b-2)=5/3.
How to proceed. I am stuck at the cross multiplying and finding out both a and b.

anonymous · Answer

Wait, are you given the information that the two equations have an infinite number of solutions?

anonymous · Answer

Yes! @genius12

anonymous · Answer

What is the a1/a2 = b1/b2 = c1/c2 for?

anonymous · Answer

nvm I got it.

anonymous · Answer

We have to take the equations in the form a1x+b1y+c1=0;a2x+b2y+c2=0;

anonymous · Answer

$$\bf \frac{ -3 }{ b-2 }=\frac{ 5 }{ 3  } \implies b-2=\frac{ -9 }{ 5 } \implies b = \frac{ -9 }{ 5 }+2=\frac{ 1 }{  }$$$$\bf \frac{ 2a-1 }{ 3 }=\frac{ 5 }{ 3 } \implies 2a-1=5 \implies a = \frac{ 5 +1}{ 2 }=3$$

anonymous · Answer

b=1/5, the 5 doesn't show up for some reason lol.

anonymous · Answer

@bajji

anonymous · Answer

@genius12 Thanks a lot!! :D