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North CarolinaMaths

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.

Why does replacing one equation with a combination of the two keep the same solution?

Prove that replacing one equation in a system with the sum of it and a multiple of the other produces an equivalent system (NC.M1.A-REI.5).
An NC Math 1 EOC answer on equivalent systems (NC.M1.A-REI.5): why adding a multiple of one equation to another preserves the solution set, which is the justification behind the elimination method.
9 min answer →

How do you graph a linear inequality in two variables, and what does the shaded region mean?

Graph a linear inequality in two variables as a half-plane with the correct boundary line and shading (NC.M1.A-REI, A-CED.3).
An NC Math 1 EOC answer on graphing linear inequalities in two variables: solid versus dashed boundary lines, choosing which side to shade with a test point, and reading the half-plane as a solution set.
10 min answer →

How do you turn a real situation with two conditions into a system and interpret the solution?

Model situations with systems of equations or inequalities, represent constraints, and interpret solutions as viable or non-viable (NC.M1.A-CED.3, A-REI.6).
An NC Math 1 EOC answer on modeling with systems (NC.M1.A-CED.3, A-REI.6): building two equations from two conditions, representing constraints with inequalities, solving, and judging whether a solution is viable in context.
11 min answer →

How do you solve a system of two linear equations using substitution or elimination?

Solve systems of two linear equations in two variables algebraically by substitution and elimination (NC.M1.A-REI.6).
An NC Math 1 EOC answer on solving systems algebraically (NC.M1.A-REI.6): the substitution method, the elimination method, choosing between them, and recognizing no-solution and infinite-solution systems.
11 min answer →

How does the intersection of two graphs give the solution of a system or equation?

Solve systems by graphing and explain why the x-coordinates of intersections of y = f(x) and y = g(x) solve f(x) = g(x) (NC.M1.A-REI.11, A-REI.6).
An NC Math 1 EOC answer on solving systems by graphing (NC.M1.A-REI.11, A-REI.6): the intersection as the solution, reading it from a graph, why intersections solve f(x) = g(x), and the three cases of one, none, or infinite solutions.
10 min answer →