8.FGR.7Systems of Linear Equations

Expectations

• 8.FGR.7.1

  Interpret and solve relevant mathematical problems leading to two linear equations in two variables.

• 8.FGR.7.2

  Show and explain that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because the points of intersection satisfy both equations simultaneously.

• 8.FGR.7.3

  Approximate solutions of two linear equations in two variables by graphing the equations and solving simple cases by inspection

• 8.FGR.7.4

  Analyze and solve systems of two linear equations in two variables algebraically to find exact solutions.

• 8.FGR.7.5

  Create and compare the equations of two lines that are either parallel to each other, perpendicular to each other, or neither parallel nor perpendicular.

Georgia Milestones coverage

• Mathematics Grade 8 (EOG) · Functional & Graphical Reasoning

  Justify and use various strategies to solve systems of linear equations to model and explain realistic phenomena.

  about 12% of the test · 7 points

What mastery looks like

Georgia's Achievement Level Descriptors. The levels are cumulative: each includes the ones before it. Proficient is on grade level.

Beginning

Describe a mathematical problem that involves two linear equations. Given the graph of a set of linear equations, identify the point of intersection of the lines as the solution to the system. Recognize from a graph that there is no solution to a system of equations formed by parallel lines.

Developing

Create a table or graph to help interpret a mathematical problem relating two linear equations. Given the solution to a system of equations, show mathematically that the given solution is the point of intersection. Identify the approximate solution to a system of linear equations from the graph of the system. Given the equations for a system of linear equations, determine whether the graphed lines will be parallel, perpendicular, or neither parallel nor perpendicular.

Proficient

Compare different scenarios leading to two linear equations and make inferences relating to the given mathematical problem. Explain the significance of the intersection of the graph of a system of linear equations within the given context of the question. Given a system of linear equations and (x, y) values for each of the equations, approximate the solution to the system of equations. Solve systems of two linear equations in two variables algebraically to find exact solutions. Given the equation of a line, create an equation for a line that is parallel or perpendicular to the given line.

Distinguished

Solve realistic problems involving systems of linear equations and interpret the solutions in relation to the problem.