Question

find the value of 'k' for which the following system of equations represents a pair of coincident lines: x+2y=3; (k-1)x+(k+1)y=k+3​

Answer 1

Answer:

if we have two linear equation in two variable as;

a1x + b1y + c1=0

a2y +b2y+c2= 0

then , condition for coincident is;

a1/a2=b1/b2=c1/c2.

so for the given equations to be coincident;

1/(k-1)=2/(k+1)=3/(k+3)

taking;

1/(k-1)=2/(k+1)

k+1=2k-2

k=3

I hope it would help you.

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Answer 2

Answer:

Applying condition of coincident lines

$\frac{1}{k - 1 } = \frac{2}{k + 1} = \frac{3}{k + 3}$

solving them we get

k=3

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