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
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find where two linear equations are true at the same time. They solve exactly with algebra and estimate solutions from graphs when needed.
What Mastery Looks Like
- Students solve a pair of linear equations by substitution, elimination, or graphing. They check the solution in both equations and identify one solution, no solution, or infinitely many solutions.
Common Misconceptions
- Students may confuse the intersection point with an intercept or switch the x and y values. They may also miss no-solution and infinitely-many-solutions cases, or treat a graph estimate as exact.
How to Assess It
- Give students the system y = 2x + 1 and y = -x + 7. Ask them to solve exactly, verify the ordered pair, and explain what the graph would show.
Lesson moves
Ways to Teach It
Use string or tape to model two lines on a coordinate grid, then record and verify their intersection point.
Ask students to compare substitution, elimination, and graphing for one system, then write which method is most efficient and why.
Run a matching game with system cards, graph cards, solution cards, and cards labeled no solution or infinitely many solutions.
Model two phone plans with linear equations, then find when their total costs are equal and interpret the intersection.
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Printable HSA-REI.C.6 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSA-REI.C.6, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.8.EE.C.8
Solving high school linear systems depends on knowing that equation pairs share solution points and can be solved algebraically or graphically.
- CCSS.Math.Content.8.EE.C.7
Solving one-variable linear equations carries into substitution or elimination after a system is reduced to a single equation.
- CCSS.Math.Content.HSA-REI.D.10
Solving systems by graphing relies on seeing each line as all solutions and intersections as shared solutions.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.HSA-REI.C.7
Linear systems introduce simultaneous solutions and graph intersections, which carry over when one equation becomes quadratic.
- CCSS.Math.Content.HSA-REI.C.8
Solving two-variable systems develops recognizing coefficients, constants, and solution sets that are organized into matrix and vector form.
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