Students will deepen their algebraic understanding of equivalent expressions by determining the solution to a system of linear equations. They also begin to extend their understanding of solution from a single value to a point or a set of points. Previously students have solved multistep linear equations; in this unit, they use graphs, tables, or algebraic methods to determine or estimate a solution to a system of equations. This work builds toward solving nonlinear equations, solving systems of inequalities, and systems of nonlinear equations in Algebra 1 as well as using systems to model and solve problems in high school math courses. Students typically struggle with understanding a solution as an ordered pair  or set of ordered pairs  and applying properties of equality to more complicated expressions.
Key Concepts:
 Solutions to a system of linear equations in two variables satisfies both equations simultaneously.
 The solution to a system of linear equations may be shown as the intersection of the graphs of each equations. This solution may estimated using a graph.
 Properties of equality, especially the transitive property, allow us to solve systems of linear equations algebraically.
 We can graph to estimate solutions and solve simple systems by inspection.
 We can write and solve systems of linear equations in two variables to solve problems with multiple simultaneous constraints.
Prior Knowledge Needed:
 Understanding solution as value/ordered pair that makes equation true.
 Use properties of equality to solve a linear equation.
 Represent a linear relationship with a graph.
 Understanding point on a graph of a line as a solution that makes equation true statement.
 Write an equation to represent a relationship between two quantities.
Units on the Horizon:
 Solving nonlinear equations
 Solving systems of linear inequalities
 Solving nonlinear systems
 Systems of inequalities
Lessons

Lesson objective: Understand that a solution for a system of two equations (conditions) is an ordered pair of values that makes both equations true. Students bring prior knowledge of solutions of linear equations from 8.EE.C.7. This prior knowledge is e...

Lesson objective: Determine if an ordered pair is a solution to a system with two variables and two conditions, often represented by two equations. This lesson helps to build procedural skill with checking solutions to systems of equations. Equations an...

Lesson objective: Understand that a point of intersection between two lines on a graph represents a solution to a system of the two equations. Students bring prior knowledge of graphing functions and linear equations from 8.F.A.1 and 8.F.B.4. This prior...

Lesson objective: Solve systems of equations by using a graph. This lesson helps to build procedural skill with graphing and solving systems of equations. A graph is used here because it supports a visual understanding of a solution to a system of equat...

Lesson objective: Apply graphs to solve systems of equations with a realworld context. This lesson provides an opportunity for students to apply their knowledge and understanding of graphs and systems of equations to a reallife situation. Students are...

Lesson objective: Understand that properties of equality can be applied to write one variable equations that will solve for the values of variables in a system of equations. Students bring prior knowledge of equivalent equations from 7.EE.A.2 and 7.EE.B...

Lesson objective: Write and solve equations in one variable to solve systems of equations by substituting equivalent terms for the other variable. This lesson helps to build procedural skill with solving systems of equations. Equations are used here bec...

Lesson objective: Solve systems of equations by substituting equivalent expressions for a variable to write and solve an equation for the other variable. This lesson helps to build procedural skill with substituting equivalent expressions. Equations are...

Lesson objective: Solve systems of equations by first rewriting an equation in order to determine an equivalent expression. This lesson helps to build procedural skill with using equations to solve systems. Equations are used here because they support r...

Lesson objective: Apply systems of equations to solve realworld problems. This lesson provides an opportunity for students to apply their knowledge and understanding of solving systems of equations to a reallife situation. Students are asked to comple...

Lesson objective: Determine the number of solutions a system of equations has. Students bring prior knowledge of number of solutions of a system on a graph from 8.EE.C.8a. This prior knowledge is extended to equations as students use the slope and yint...

Lesson objective: Solve systems by inspection, indicating the number of solutions. This lesson helps to build fluency with finding the number of solutions without solving or graphing. Tables, graphs, and equations are used here because recognizing the s...

Lesson objective: Write and solve systems of equations from a description, especially those that lead to equations in standard form. Students bring prior knowledge of writing one or more variable equations from 7.EE.B.4 and 8.F.B.4. This prior knowledge...

Lesson objective: Write systems from a description, and determine the best way to solve based on their structure. This lesson helps to build procedural skill with solving by substitution or by other algebraic methods. Verbal descriptions and equations a...

Lesson objective: Apply knowledge of systems to solve a simple system with multiple variables and constraints. This lesson provides an opportunity for students to apply their knowledge and understanding of twovariable systems to a reallife situation. ...