Test \((2,1)\) in \(y=x^{2}-3\) and \(y=2x+1\). Evaluate each equation independently and explain why satisfying only one equation is insufficient for a system solution.

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Candidate (2, 1): 1 = 2² − 3 is true; 1 = 2(2) − 3 is true; therefore it is a solution.

Candidate (2, 1): 1 = 2² − 3 is true; 1 = 2(2) + 1 is false; therefore it is a solution.

Candidate (2, 1): 1 = 2² − 3 is true; 1 = 2(2) + 1 is false; therefore it is not a solution.

Candidate (2, 1): 1 = 2² + 3 is false; 1 = 2(2) + 1 is false; therefore it is not a solution.

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Curriculum context

Course: Math II
Standard: A-REI.7
Category: Algebra
Domain: Reasoning with Equations and Inequalities
Objective: Solve simple linear-quadratic systems algebraically and graphically.
Problem type: Check a candidate point in a linear-quadratic system