For what value of `k` , the following pair of linear equations has infinitely many solutions? `10 x+5y-(k-5)=0,\ \ \ \ 20 x+10 y-k=0`

Explanation

For infinitely many solutions, we have ` (a_1)/(a_2) = (b_1)/(b_2) =(c_1)/(c_2)`.
` therefore (10)/(20) = (5)/(10) = ( k - 5)/(k) rArr ( k - 5)/(k) = (1)/(2) rArr 2k - 10 = k rArr k = 10`.