Show that the following system of equations has an infinite number of solutions. x+y+2z = -2; 3x-y+14z=6; x+2y=-5

Substitute values of one equation into another. 

(1) x+y+2z = -2; (2) 3x-y+14z=6; x+2y=-5 (3).

Substitute x in (1) and (2) from (3).

We get -y+2z=3 in (1). 

We get -7y+14z=21 in (3).

Since (3) is (1)*7, we can conclude that the system has infinite solutions.