Question

Find the values of a and b for which the following system of equations has infinitely many solutions:
(i) (2a-1)x-3y=53x+(b-2)y=3(ii) 2x-(2a+5y)y=5(2b+1)x-9y=15(iii) (a-1)x+3y=26x+(1-2b)y=6(iv) 3x+4y=12(a+b)x+2(a-b)y=5a-1(v) 2x+3y=7(a-b)x+(a+b)y=3a+b-2(vi) 2x+3y-7=0(a-1)x+(a+1)y=(3a-1)(vii)2x+3y=7(a-1)x+(a+2)y=3a

Answer 1

a = 3  , b = 1/5

Step-by-step explanation:

a₁x + b₁y = c₁

a₂x + b₂y = c₂

has infinite solutions

if a₁/a₂ = b₁/b₂ = c₁/c₂

(i)

(2a-1)x - 3y = 5

3x + (b-2)y = 3

infinite solution iff

(2a - 1)/3  =  -3/(b - 2)  = 5/3

=> 2a - 1 = 5

=> 2a = 6

=> a = 3

-3/(b - 2)  = 5/3

=> -9 = 5b - 10

=> 5b = 1

=> b = 1/5

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Answer 2

Answer:

a = 3  , b = 1/5

Step-by-step explanation: