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
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the ordered pair that makes both equations true. They solve using substitution or elimination, estimate the intersection from a graph, and identify simple cases by inspection.
What Mastery Looks Like
- Students choose substitution or elimination and find an accurate ordered pair. They check the pair in both equations and connect it to the graph’s intersection. They recognize no solution or infinitely many solutions from the equations.
Common Misconceptions
- Students often make sign errors during elimination or fail to multiply every term in an equation. They may think parallel lines intersect or call coincident lines two solutions. They may also treat a rough graph estimate as an exact answer.
How to Assess It
- Exit ticket: Solve 2x + y = 7 and x - y = 2 algebraically, then sketch both lines and circle their intersection. Explain why the ordered pair works in both equations.
Lesson moves
Ways to Teach It
Plot two equations on separate transparencies, overlay them, and mark the intersection before checking it with elimination.
Ask students to explain when elimination is faster than substitution for a given pair of equations.
Play System Match by pairing equation cards with solution, no-solution, or infinitely-many-solutions cards.
Compare two phone plans with different fees and rates, then find when their total costs are equal.
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Printable 8.EE.C.8b Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.8.EE.C.8b, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
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Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.8.EE.C.7b
Algebraic methods for systems often reduce to one linear equation requiring distributing, combining like terms, and solving with rational coefficients.
- CCSS.Math.Content.8.EE.C.8a
Students must know a system’s solution is the intersection point satisfying both equations before graphing or checking algebraic solutions.
- CCSS.Math.Content.8.F.A.3
Recognizing y = mx + b as a line supports graphing two equations and interpreting their intersection as the solution.
What This Unlocks
Mastery here sets students up for these next.
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Related Standards
- 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.
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