NY Next Generation Math AI-A.REI.6.a

MathGrades 9–12Solve systems of equations.

The Standard

Solve systems of linear equations in two variables both algebraically and graphically.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What Students Need to Do: Students solve two-variable linear systems in Algebra I by graphing, substitution, and elimination. They connect the algebraic solution with the intersection of the two lines.
What Mastery Looks Like: The student selects an efficient method, finds an accurate ordered pair, and verifies it in both equations. The graph and algebra agree on whether the system has one, none, or infinitely many solutions.
Common Misconceptions: Students may substitute into only one equation, combine unlike sides during elimination, or report separate x and y intercepts as the solution. They may overlook parallel or identical lines.
How to Assess It: Ask students to solve y equals 2x plus 1 and 3x plus y equals 11 by substitution and graphing, then explain why the answers match.

Lesson moves

Overlay two transparent line graphs and locate the point that satisfies both equations.
Ask students when elimination is more efficient than substitution and require a specific system example.
Play method choice with system cards, earning a point for both a sensible method and correct solution.
Compare two pricing plans by solving where their linear cost models are equal.

Keep exploring

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