Q. 234.0( 7 Votes )
Find the values of a and b for which each of the following systems of linear equations has an infinite number of solutions:
2x - 3y = 7, (a + b)x - (a + b - 3)y = 4a + b.
Answer :
Given: 2x - 3y = 7 – eq 1
(a + b)x - (a + b - 3)y = 4a + b – eq 2
Here,
a1 = 2, b1 = - 3, c1 = - 7
a2 = (a + b), b2 = - (a + b - 3), c2 = - (4a + b)
Given that system of equations has infinitely many solution
∴ 
= 
= 
= 
= 
Here,
= 
- 3×( - 4a + b) = - 7× - (a + b - 3)
12a + 3b = 7a + 7b - 21
12a - 7a = - 3b + 7b - 21
5a = 4b - 21
5a – 4b + 21 = 0 
eq 3
Also,
= 
2× - (4a + b) = - 7×(a + b)
- 8a – 2b = - 7a – 7b
- 8a + 7a = 2b – 7b
- a = - 5b
a = 5b 
eq 4
substitute – eq 4 in – eq 3
5(5b) – 4b + 21 = 0
25b – 4b + 21 = 0
21b + 21 = 0
b = 
b = - 1
substitute ‘b’ in – eq 4
a = 5( - 1)
a = - 5
∴ a = - 5, b = - 1
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