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Constants and Variables

45. If the gi...

Question

45. If the given equation has infinitely many solution, then find value of a and b: 2x + 3y = 7 (a-b)x + (a+b)y = 3a + b - 2

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2 x + 3 y = 7

(a - b) x + (a + b) y = 3 a + b - 2

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

2 x + 3 y = 7

(a + b) x + (2 a - b) y = 21

a

b

2 x + 3 y = 7

(a - b) x + (a + b) y = 3 a + b - 2

a

b

2 x - 3 y = 7

(a + b) x - (a + b - 3) y = 4 a + b

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