Find the value of \( k \) for which the following system of equations has infinitely many soluti...

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Find the value of \( k \) for which the following system of equations has infinitely many solutions.
(i) \( 4 x+7 y=10 ;(k+2) x+21 y=3 k \)
(ii) \( x+2 y+7=0,2 x+k y+14=0 \)
(iii) \( 2 x+(k-2) y=k ; 6 x+(2 k-1) y=2 k+5 \)
(iv) \( 2 x+3 y=2 ; \quad(k+2) x+(2 k+1) y=2(k-1) \)
(v) \( x+(k+1) y=5,(k+1) x+9 y=(8 k-1) \)
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