Adding the two rules of a system to remove one unknown leaves the statement 0 = 0. What does that ending mean?

1. A statement such as 0 = 0 is true no matter what values the unknowns take. 2. That means every point on the line satisfies both rules, since nothing has been ruled out. 3. Two rules satisfied by the same endless set of points describe one and the same line. 4. A system like that is dependent and has infinitely many solutions. 5. Option D describes the opposite ending, which would be a false statement such as 9 = 13. 6. Option C singles out one point, but an identity rules nothing out, so no single point can be picked out this way. 7. Option A is the common worry, but an identity is a real result rather than a slip. _Source: OpenStax College Algebra (CC BY 4.0), Ch 7 "Systems of Equations and Inequalities", section 7.1 Systems of Linear Equations: Two Variables_