Question

plz solve this problem fast

Answer 1

Consider two equations:
$a_1x+b_1y+c_1=0 \\ \\ a_2x+b_2y+c_2=0$

For the system of above two equations to have infinite possible solutions, the ratio of all coefficients must be same. 
So, we have:

$\boxed{\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}}$


Here, our two equations are:

$(2a-1)x +3y - 5 = 0 \\ \\ 3x+(b-1)y-2=0$

For infinitely many solutions, we have:

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

Let's take both equalities one at a time.


$\frac{2a-1}{3}=\frac{5}{2} \\ \\ \\ \implies 2a-1 = \frac{15}{2} \\ \\ \\ \implies 2a=\frac{15}{2}+1 \\ \\ \\ \implies 2a = \frac{17}{2} \\ \\ \\ \implies \boxed{a=\frac{17}{4}}$

Now, the other equality:

$\frac{3}{b-1} = \frac{5}{2} \\ \\ \\ \implies 6 = 5(b-1) \\ \\ \\ \implies 6 = 5b-5 \\ \\ \\ \implies 11 = 5b \\ \\ \\ \implies \boxed{b=\frac{11}{5}}$


Thus, we have obtained the values of a and b. 


Hope it helps
Purva
Brainly Community