CCSS.Math.Content.HSA-REI.C.6
The standard
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Common Core State Standards for Mathematics
What this standard means
Students need to solve two-variable linear systems using algebraic methods and graphs. They should find the point where both equations are true, not just solve each line separately. They also need to understand when a graph gives an estimate and when substitution or elimination gives an exact answer.
Mastery looks like choosing a method that fits the system, showing clear steps, and checking the solution in both equations. Students often get stuck with sign errors in elimination, graphing lines inaccurately, or thinking every system has one solution. They also need practice spotting no solution and infinitely many solutions.
Ways to teach it
- Use two colored strings on grid paper to model two lines, then mark the intersection and write the ordered pair solution.
- Prompt students: Which method would you use for this system, graphing, substitution, or elimination, and why?
- Give one system and ask students to solve it two ways, then check the ordered pair in both original equations.
- Compare two phone plans with monthly fees and per-gigabyte costs, then find when the total costs are equal.
Plan a lesson for CCSS.Math.Content.HSA-REI.C.6
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Related standards
- CCSS.Math.Content.8.EE.C.8
Analyze and solve pairs of simultaneous linear equations.
- CCSS.Math.Content.8.EE.C
Analyze and solve linear equations and pairs of simultaneous linear equations.
- CCSS.Math.Content.HSA-REI.C.7
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
- CCSS.Math.Content.8.EE.C.8b
Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.