If possible please type the equations one above the other:
17 = 11y + 12x
12x + 11y = 14
to make the easier to compare. I see immedately that both equations have the terms 11y+12x on one side with a constant (14 or 17) on the other. Because of this, we know immediately that the lines are parallel and never intersect and thus have no solution. Substitution will not give you a diff result.