CCSS.Math.Content.HSA-REI.C.7
The standard
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
Common Core State Standards for Mathematics
What this standard means
Students need to solve systems where one equation is linear and the other is quadratic, such as a line with a parabola or circle. They should solve by substitution, then interpret the solutions as intersection points on a graph.
Mastery means students can find zero, one, or two solutions, write ordered pairs, and check them in both equations. Common trouble spots are substitution errors, forgetting both x and y coordinates, mishandling squared terms, and not connecting algebraic answers to the graph.
Ways to teach it
- Have students graph a line and parabola on grid paper, mark intersections, then verify each point by substitution.
- Ask students to explain why a line can hit a circle zero, one, or two times, using a quick sketch.
- Give one system and ask students to solve by substitution, then state how many intersection points the graph should show.
- Use a map-style problem where a straight road crosses a circular sprinkler zone, and students find the entry and exit points.
Plan a lesson for CCSS.Math.Content.HSA-REI.C.7
Generate a complete lesson plan aligned to this standard, with objectives, activities, and materials. Free, no account needed.
Related standards
- CCSS.Math.Content.HSA-REI.B.4
Solve quadratic equations in one variable.
- 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.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.