CCSS.Math.Content.8.EE.C.8b
The standard
Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.
Common Core State Standards for Mathematics
What this standard means
Students need to solve a pair of linear equations by using algebra, usually substitution or elimination, and connect that answer to the point where two lines meet on a graph. They also need to estimate the solution from a graph and spot easy cases by looking at the equations.
Mastery means students can choose a method, show clean steps, and explain whether the system has one solution, no solution, or infinitely many solutions. Common trouble spots are sign errors during elimination, solving for the wrong variable, graphing with poor scale, and thinking every system must have one ordered-pair answer.
Ways to teach it
- Use two colored strings on coordinate grid paper to model two lines, then have students mark and name the intersection point.
- Ask students to explain which method they would use for 2x plus y equals 9 and x minus y equals 3, and why.
- Give one system and have students solve it by elimination, then check the ordered pair in both equations.
- Compare two phone plans with monthly fees and per-gigabyte costs, then find when the total costs are the same.
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Related standards
- CCSS.Math.Content.8.EE.C.8c
Solve real-world and mathematical problems leading to two linear equations in two variables.
- CCSS.Math.Content.HSA-REI.C.6
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
- 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.