CCSS.Math.Content.8.EE.C.8a
The Standard
Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students graph two linear equations on the same coordinate plane. They locate the intersection and explain why its coordinates make both equations true.
What Mastery Looks Like
- Students identify the intersection as the ordered pair that works in both equations. They can read it from a graph and confirm it by substitution.
Common Misconceptions
- Students may use where a line crosses an axis instead of where the two lines cross. They may also reverse the coordinates or check the point in only one equation.
How to Assess It
- Give students y = 2x + 1 and y = -x + 7. Ask them to graph both, name the solution, and verify it in each equation.
Lesson moves
Ways to Teach It
Give pairs graph paper and colored pencils to graph two equations, mark the intersection, and test its coordinates in both equations.
Ask students to write why a point on only one line cannot solve the pair of equations.
Play Intersection Match by pairing equation cards with graph cards and solution cards, then checking each match by substitution.
Compare two phone plans with different fees and monthly costs, then graph when both plans cost the same.
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Printable 8.EE.C.8a Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.8.EE.C.8a, 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.6.NS.C.8
Graphing points in the coordinate plane supports seeing an intersection point as the ordered pair shared by both line graphs.
- CCSS.Math.Content.6.EE.B.5
Students must understand solutions as values that make equations true before seeing intersection points as values satisfying both equations.
- CCSS.Math.Content.8.F.A.3
Recognizing y = mx + b graphs as lines supports seeing two linear equations meet at points satisfying both equations.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.8.EE.C.8b
Students must know a system’s solution is the intersection point satisfying both equations before graphing or checking algebraic solutions.
- CCSS.Math.Content.8.EE.C.8c
Interpreting a system’s solution as one point satisfying both equations supports modeling and solving two-equation problems.
- CCSS.Math.Content.HSA-REI.D.11
The idea that an intersection satisfies both equations extends from linear systems to solving f(x)=g(x) graphically.
Keep exploring
Related Standards
- CCSS.Math.Content.HSA-REI.D.10
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be...
- 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.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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