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Question

Find the values of a and b for which the following system of equations has infinitely many solutions:

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

     3x + (b - 2) y = 3

(ii) 2x - (2a + 5) y = 5

     (2b + 1) x - 9y = 15

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

      6x + (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

(viii)  x + 2y = 1

         (a - b) x + (a + b) y = a + b - 2

(ix)   2x + 3y = 7

       2ax + ay = 28 - by


Solution

(i) a = 3, b = 15

(ii) a = -1, b = 52

(iii) a = 3, b = -4

(iv) a = 5, b = 1

(v) a = 5, b = 1

(vi) a = 5

(vii) a = 7

(viii) a = 3, b = 1

(ix) a = 4, b =8

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