Q. 264.3( 4 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, 2ax + (a + b)y = 28
Answer :
Given: 2x + 3y = 7 – eq 1
2ax + (a + b)y = 28 – eq 2
Here,
a1 = 2, b1 = 3, c1 = - 7
a2 = 2a, b2 = (a + b), c2 = - 28
Given that system of equations has infinitely many solution
∴ 
= 
= 
= 
= 
Here,
= 
3× - 28 = - 7×(a + b)
- 84 = – 7a – 7b
7a + 7b – 84 = 0
a + b – 12 = 0 
eq 3
Also,
= 
2× - 28 = - 7×2a
– 56 = – 14a
14a = 56
a = 
a = 4 
eq 4
substitute – eq 4 in – eq 3
4 + b – 12 = 0
a + b – 12 = 0
b – 8 = 0
b = 8
∴ a = 4, b = 8
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