Common core Algebra
Unit 6: Systems of linear equations and inequalities
15 Days
CCSS
A.CED.3 Represent constraints by equations or inequalities, and by systems of equations
and/or inequalities, and interpret solutions as viable or non-viable options in a modeling
context. For example, represent inequalities describing nutritional and cost constraints on
combinations of different foods.
Mathematical Scope
Examples
Level 3
I can write a system of equations/inequalities given
a situation.
Level 4
I can write the constraints to an optimization
problem given the situation. (Linear Programming)
I can determine the optimal solution given three
constraints.
I can write and solve a system of equations.
Level 5
I can write the inequality given two points on the
line and two other solutions of the inequality (not on
the line).
Domain
Solve systems of equations.
Build on student experiences graphing and solving systems of linear equations from middle
school to focus on justification of the methods used. Include cases where the two equations
describe the same line (yielding infinitely many solutions) and cases
where two equations describe parallel lines (yielding no solution); connect to
GPE.5 when it is taught in Geometry, which requires students to prove the slope criteria for
parallel lines.
CCSS
A.REI.5 Prove that, given a system of two equations in two variables, replacing one
equation by the sum of that equation and a multiple of the other produces a system with
the same solutions.
Mathematical Scope
Examples
Level 3
I can solve a system of equations where the pair of
coefficients of one variable are opposite.
Level 4
I can solve a system of equations where I use a
multiplier on one equation.
I can solve a system of equations where I use a
multiplier on both equations.
I can identify systems where there are no solutions or
infinite solutions.
Level 5
I can write a system of equations from a given
situation and solve it.
CCSS
A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs),
focusing on pairs of linear equations in two variables.
Mathematical Scope
Examples
Level 3
Given a graph of a system of linear equations, I can
identify the solution.
I can graph two equations (in slope-intercept form)
and find the exact solution.
Level 4
When graphing a system, I can recognize systems
that have no solution or infinite solutions.
I can graph two equations and find the approximate
solutions.
Level 5
Given a real-life situation involving systems, I am able
to interpret the solution in context.
CCSS
A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane
(excluding the boundary in the case of a strict inequality), and graph the solution set to a
system of linear inequalities in two variables as the intersection of the corresponding
half-planes.
Mathematical Scope
Examples
Level 3
I can identify a point that is a solution of the system of
inequalities given the graph.
I can identify a point that is not a solution of the
system of inequalities given the graph.
Level 4
I can graph a system of linear inequalities in two
variables.
Level 5
I can write and graph the constraints for a linear
programming problem and use the results to solve a
problem involving maximization/minimization
problem.