The given system of equations:
5x + 2y = 2k
⇒ 5x + 2y - 2k = 0 ….(i)
And, 2(k + 1)x + ky = (3k + 4)
⇒ 2(k + 1)x + ky - (3k + 4) = 0 …(ii)
These equations are of the following form:
a1x+b1y+c1 = 0, a2x+b2y+c2 = 0
where, a1 = 5, b1= 2, c1 = -2k and a2 = 2(k + 1), b2 = k, c2 = -(3k + 4)
For an infinite number of solutions, we must have:
Hence, the given system of equations has an infinite number of solutions when k is equal to 4.
