Question

For which values of a and b does the following pair of linear equations have an

infinite number of solutions?

2x + 3y = 7

(a – b) x + (a + b) y = 3a + b – 2​

Answer 1

2x +3y =7 and (a-b)x + (a+b)y = 3a+b-2

now a and b have infinite solution when a1/a2 =b1/b2= c1/C2

now a1=2 a2= (a-b) b1= 3 b2= (a+b) c1=-7 (2x+3y-7=0) c2 = -(3a+b-2)

2/a-b = 3/a+b = -7/ -(3a+b-2)

2/a-b=3/a+b = 2a+2b=3a+3b (by cross multiplication)

a-5b=0 (1)

3/a+b= 7 / 3a+b-2= 9a+3b-6=7a+7b (by cross multiplication)

2a-4b=6 (2)

multiplying (1) by 2

2a-10b=0 (3)

subtracting 3 from 2

2a-2a+(-10b)-(-4b) =0-6

-10b+4b =-6 ----- -6b=-6------- b=1

putting this value in 3 we get

2a-10(1)=0------- 2a =10----- a=5

so for a=5 and b=1 the value of given equation will have infinite solution

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