Determine the values of $a$ and $b$ , so that the following system of linear equations have infinitely many solutions:
$(2 a - 1) x + 3 y - 5 = 0$
$3 x + (b - 1) y - 2 = 0$

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Solution

Given
$(2 a - 1) x + 3 y - 5 = 0$
$3 x + (b - 1) y = 2$
Since they have infinite no. of solution ,
$\frac{2 a - 1}{3} = \frac{3}{b - 1} = \frac{- 5}{- 2}$
$\frac{2 a - 1}{3} = \frac{3}{b - 1} = \frac{5}{2}$
$4 a - 2 = 15$
$a = \frac{17}{4}$
$6 = 5 b - 5$
$5 b = 11$
$b = \frac{11}{5}$

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