Question

Determine for what values of x and y are the following equalities always true.

(k+1)x-(2k+3)y-3k-5=0

Answer 1

(k+1)x-(2k+3)y-3k-5=0
kx + x - 2ky - 3y - 3k - 5 = 0
(x - 2y) k + (x - 3y) = 3k + 5

therefore
x - 2y = 3
x - 3y = 5

Subtract 2 equations
y = -2
x = -1