Question

find the value of a and b for which the following system of linear equations have infinitely many solution:3x-(a+1)y=2b-1 ; 5x +(1-2a)y=3b

Answer 1

3 -(a+1)
-- = -----
5 (1-2a)
by crossmultiplying
we get
3(1-2a) = -5(a+1)
3 - 6a = -5a -5
3 +5 = -5a + 6a
8 = a

for B
-(a+1) 2b - 1
----- = --------
(1-2a) 3b

by crossmultiplying
-3ab - 3b = 2b( 1-2a) -1(1-2a)
put a = 8
-3*8b - 3b = 2b - 2*8b - 1 + 2*8
-24b - 3b = 2b - 16b - 1 +16
-27b = -14b +15
-27b + 14b = 15
-13b = 15
b = -15
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13