Question

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Q16

Answer 1

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Answer 2

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• x+(k+1)y-4=0
• (k+1)x+9y-(5x+2)=0

The system of equations is of the form

• a1x+b1y+c1=0
• a2x+b2y+c2=0

where

• a1 = 1, b1 = k+1, c1 = 4

and

• a2 = k+1, b2=9, c2= -(5k+2)

e solution, we must have

= C1/C2

K+1/9 = -4/-(5k+2)

= k+1/9 and k+1/9 = 4/5k+2

= 9 = (k+1)² and (k+1) (5k+2) =36

= 9=k²+1+2k and 5k²+2k+5k+2=36

= k²+2k+1-9=0 and 5k²+7k+2-36=0

= k²+2k+1-8=0 and 5k²+7k-34=0

= k²+4k-2k-8=0 and 5k²+17k-10k-34=0

= k(k+4) -2(k+4) = 0 and (5k+17)-2(5k+17) =0

= (k+4) (k-2) = 0 and (5k+1) (k-2)=0

= (k= -4 or k=2) and (k = -17/5 or k=2)

= k=2 satisfies both the conditions

Hence, the given system of equations will have infinitely many solutions, if k=2

HOPE IT IS HELPFUL TO YOU!!