Question

For what value of k does the following pair of linear equations have infinitely many solutions?

10x + 5y – (k – 5) = 0 and 20x + 10y – k = 0

Answer 1

For infinitely many solutions, we have `(a_1)/(a_2) = (b_1)/(b_2) = (c_1)/(c_2)`.

∴ `10/20 = 5/10`

= `(k - 5)/k`

⇒ `(k - 5)/k = 1/2`

⇒ 2k – 10 = k

⇒ k = 10