The point (2,3) lies on the graph of the linear equation 3x - (a -1)y =2a -1. If the same point also lies on the graph of the linear equation 5x + (1-2a)y = 3b, then find the value of b. -Maths 9th

The point (2,3) lies on the graph of the linear equation 3x - (a -1)y =2a -1. If the same point also lies on the graph of the linear equation 5x + (1-2a)y = 3b, then find the value of b. -Maths 9th
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Given, point (2,3) lies on the line. So, the point (2, 3) is the solution of 3x - (a -1) y = 2a - 1 On putting x = 2 and y = 3 in given solution.  ∴ 3 × 2 - (a-1) × 3 = 2a - 1  ⇒ 6 - 3a + 3 = 2a - 1 ⇒  - 3a - 2a = - 1 - 3 - 6 ⇒ -5a = -10 ⇒ a = 2  Also, (2, 3) is the solution of 5x + (1- 2a) y = 3b. on putting x = 2 and y = 3 in given equation  ∴ 5 × 2 + (1 - 2a) × 3 = 3b  --- i) Now, putting the value of a = 2 in eq. (i) we get  5 × 2 + (1 - 2 × 2) × 3  = 3b  ⇒ 10 - 9 = 3b  ⇒  1 = 3b ⇒  1 / 3 = b Hence, the value of b is 1 / 3.
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