Question

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Find the the value of a and b for which the following systems of linear equation was infinite no of solutions:

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Answer 1

Heya!

refer the attachment for the answer!

Answer 2

Answer:

a = -1/3

b = -4

Step-by-step explanation:

(a - 1)x  + 3y  = 2

bx + (1 - 2b)y  = 6

(a - 1)x  + 3y  = 2

=> 3y = (1-a)x + 2

=> y = (1/3)(1-a)x  + 2/3

bx + (1 - 2b)y  = 6

bx - 6 = (2b -1)y

=> y = (b/(2b-1)) x - 6/(2b-1)

To have infinite solutions line should have same equation

=> 2/3 = -6/(2b - 1)

=> 2b - 1 = -9

=> 2b = -8

=> b = -4

(1/3)(1-a) = b/(2b-1)

=> (2b - 1)(1-a) = 3b

=> (-9)(1-a) = -12

=> 1-a = 4/3

=> a = 1 - 4/3

=> a = -1/3