Final answer:
The correct final line of Giovanni's algebraic solution for a system of equations with parallel lines would be a contradiction like -5 = -5 + 1, which indicates that there are no solutions since parallel lines do not intersect.
Step-by-step explanation:
If Giovanni solves a system of equations and concludes that the lines are parallel, the final line of his solution would indicate that there is no point of intersection between the two lines. In other words, the system has no solution, which is represented algebraically by an equation that is a contradiction.
The correct final line of his solution among the options provided would therefore be D. -5 = -5 + 1. This is because it simplifies to -5 = -4, which is a contradiction and indicates that there is no solution to the system, corresponding to parallel lines with no intersection.
In contrast, options A, B, and C (5 = 5, -5 = -5, 11 = 11) represent identities, which are true for any values and imply that the system has an infinite number of solutions, characteristic of coincident lines rather than parallel lines.