Question

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Find the values of a and b for which the system of equations has infinitely many solutions. ( a -1) x + 3y= 2; 6x + ( 1 -2b) y =6

Answer 1

Answer:

Given pair of linear equations:

3x-(a+1)y=2b-1......................1

5x+(1-2a)y=3b......................2

Here we have,

a1=3 , a2=5 , b1=-a-1 , b2=1-2a , c1=2b-1 , c2=3b

The condition required for which pair of linear equation has infinitely many solution is,

a1/a2 = b1/b2 = c1/c2

By putting all values we have,

3/5 = (-a-1)/(1-2a) = (2b-1)/(3b)

3/5 = (-a-1)/(1-2a) and 3/5 = (2b-1)/(3b)

3-6a = -5a-5 and 9b =10b-5

a = 8 and b=5

For value of a=8 and b=5 ,the given pair of linear equation has infinitely many solutions.