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Systems of Equations and Inequalities

4 dot points across 4 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 how do you find the solution region of a system of inequalities?

Graph linear inequalities in two variables on the coordinate plane and find the solution set of a system of linear inequalities as the overlap of the half-planes (TN A1.A.REI.D.8, A1.A.REI.D.9).
A TNReady Algebra I answer on graphing linear inequalities in two variables (TN A1.A.REI.D.8, D.9), solid versus dashed boundaries, shading the correct half-plane, and finding the overlap region for a system.
10 min answer →

How do you solve a system made of a linear equation and a quadratic equation, both algebraically and graphically?

Solve a simple system consisting of a linear equation and a quadratic equation in two variables, algebraically and graphically (TN A1.A.REI.C.7).
A TNReady Algebra I answer on linear-quadratic systems (TN A1.A.REI.C.7), substituting the line into the parabola, solving the resulting quadratic, and interpreting zero, one, or two intersection points.
10 min answer →

How do you model a real-world situation with a system of equations or inequalities, and interpret the solution as viable constraints?

Represent constraints by systems of equations and inequalities and interpret solutions as viable or nonviable options in a modeling context (TN A1.A.CED.A.3).
A TNReady Algebra I answer on modeling with systems (TN A1.A.CED.A.3), writing two equations or inequalities from a context, solving, and interpreting the solution as a viable option.
10 min answer →

How do you solve a system of two linear equations by graphing, substitution, and elimination, and what does the solution represent?

Solve systems of two linear equations in two variables exactly and approximately by graphing, substitution, and elimination, and justify the elimination method (TN A1.A.REI.C.5, A1.A.REI.C.6).
A TNReady Algebra I answer on solving systems of linear equations (TN A1.A.REI.C.5, C.6) by graphing, substitution, and elimination, and recognizing one, none, or infinitely many solutions.
11 min answer →