Question

For what values of a and b does the following pair of equations have an infinite numbers of solutions.       2x+3y=7, a(x+y)-b(x-y)=3a+b-2​

Answer 1

Answer:

2x + 3y = 7

7ax −bx + ay + by = 3a + b − 2

(or) 2x + 3y = 7 …………(1)

7 …………(1)(a−b) x + (a+b) y = 3a + b − 2 ………….(2)

Given: the pair of linear equations have infinite number of solutions

2 3 7

a – b a – b. 3a + b – 2

2 = 3

a – b a + b

3 = 7

a + b 3a + b – 2

= 2a + 2b = 3a − 3b

= − a = − 5b

= a = 5b

= 3 (3a + b − 2) =7 (a + b)

= 9a + 3b − 6 = 7a + 7b

= 2a − 4b − 6 = 0

= a − 2b = 3

= Put a = 5b in a − 2b = 3 we get

= 5b − 2b = 3

= 3b = 3 or b = 1

1∴a = 5 × 1 = 5, b = 1

1Hence a = 5, b = 1.