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Systems of Equations and Inequalities

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you graph a linear inequality in two variables, and which side of the boundary line do you shade?

Graph a linear inequality in two variables as a half-plane, using a solid or dashed boundary and shading the correct side (LA A1: A-REI.D.12).
A Louisiana LEAP 2025 Algebra I answer on graphing a two-variable linear inequality (LA A1: A-REI.D.12): solid versus dashed boundary lines, choosing the shaded half-plane, and using a test point.
9 min answer →

How do you set up a system of equations or inequalities to model a real-world situation and answer the question?

Represent constraints by a system of equations or inequalities and interpret solutions as viable or nonviable options in context (LA A1: A-CED.A.3).
A Louisiana LEAP 2025 Algebra I answer on modeling with systems (LA A1: A-CED.A.3): writing two equations from a word problem, representing constraints with inequalities, and judging which solutions are viable.
10 min answer →

How do you solve a system of two linear equations using substitution and elimination, and what does the solution mean?

Solve systems of two linear equations in two variables algebraically using substitution and elimination (LA A1: A-REI.C.6).
A Louisiana LEAP 2025 Algebra I answer on solving systems algebraically (LA A1: A-REI.C.6): the substitution method, the elimination method, choosing between them, and recognizing no-solution and infinite-solution systems.
10 min answer →

How do you solve a system by graphing, and how does the intersection point relate to the algebraic solution?

Solve a system of two linear equations by graphing and recognize that the intersection point is the solution (LA A1: A-REI.C.6, A-REI.D.11).
A Louisiana LEAP 2025 Algebra I answer on solving systems by graphing (LA A1: A-REI.C.6, D.11): plotting both lines, reading the intersection, and seeing parallel and identical lines as the special cases.
9 min answer →

How do you graph a system of linear inequalities, and what does the overlapping region represent?

Graph the solution set of a system of two or more linear inequalities as the overlap of the half-planes (LA A1: A-REI.D.12).
A Louisiana LEAP 2025 Algebra I answer on systems of linear inequalities (LA A1: A-REI.D.12): graphing each inequality, finding the overlapping solution region, and testing whether a point satisfies all constraints.
9 min answer →