Students explore what happens when you consider two linear equations simultaneously, and explore the many rich applications that can be modeled with systems of linear equations in two variables.
In Unit 6, eighth-grade students explore what happens when you consider two linear equations simultaneously. They graph two lines in the same coordinate plane and ask themselves what coordinate points satisfy both of the equations. They consider what it means when two lines never intersect or when they overlap completely. Students learn algebraic methods that can be used to solve systems when graphing is not efficient. Using the structure of the equations in a system, students will determine if systems have one, no, or infinite solutions without solving the system (MP.7). Students also explore the many rich applications that can be modeled with systems of linear equations in two variables (MP.4).
Students will use their knowledge from previous eighth-grade units, including work with single linear equations and functions from clusters 8.EE.B and 8.F.B. They will also need to draw on concepts from sixth grade, where they understood solving an equation as a process of answering which values make an equation true.
In high school, students will continue their work with systems, working with linear, absolute value, quadratic, and exponential functions. They will also graph linear inequalities and consider what the solution of a system of linear inequalities looks like in the coordinate plane.
Pacing: 15 instructional days (11 lessons, 3 flex days, 1 assessment day)
This assessment accompanies Unit 6 and should be given on the suggested assessment day or after completing the unit.
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system of linear equations
substitution (to solve a system of equations)
elimination (linear combinations)
zero pair
infinite solutions
unique solution
no solution
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8.EE.C.8.A
Define a system of linear equations and its solution.
8.EE.C.8.A
8.EE.C.8.B
Solve systems of linear equations by graphing.
8.EE.C.8.A
8.EE.C.8.B
Classify systems of linear equations as having a unique solution, no solutions, or infinite solutions.
8.EE.C.8.C
Solve real-world and mathematical problems by graphing systems of linear equations.
8.EE.C.8.B
Solve systems of linear equations using substitution when one equation is already solved for a variable.
8.EE.C.8.B
Solve systems of linear equations using substitution by first solving an equation for a variable.
8.EE.C.8.C
Solve real-world and mathematical problems using linear systems and substitution.
8.EE.C.8.B
Solve systems of linear equations using elimination (linear combinations) when there is already a zero pair.
8.EE.C.8.B
Solve systems of linear equations using elimination (linear combinations) by first creating a zero pair.
8.EE.C.8.B
8.EE.C.8.C
Solve real-world and mathematical problems using systems and any method of solution.
8.EE.C.8.C
Model and solve real-world problems using systems of equations.
Key: Major Cluster Supporting Cluster Additional Cluster
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