CCSS.Math.Content.8.EE.C.8c
The Standard
Solve real-world and mathematical problems leading to two 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 represent each relationship with a linear equation in two variables. They solve the pair using a graph, substitution, or elimination, then explain what the solution means.
What Mastery Looks Like
- A student can turn a context or two pairs of points into two linear equations and find their intersection. They identify one solution, no solution, or infinitely many solutions, then check and interpret the result.
Common Misconceptions
- Students often reverse the slope ratio or lose a negative sign when writing an equation from two points. They may assume every pair of lines intersects once, or mistake the drawn segments for the full lines. Some find an intersection but do not check it in both equations.
How to Assess It
- Give this exit ticket: Line A passes through (0, 1) and (3, 7), while Line B passes through (0, 7) and (3, 4). Find their intersection and show your method.
Lesson moves
Ways to Teach It
On a floor coordinate grid, pairs stretch yarn through two point cards for each line, then mark and verify the intersection.
Prompt students to sketch and explain how two lines can have one solution, no solution, or infinitely many solutions.
Run a card sort matching point pairs, equations, graphs, and intersections, including parallel and identical lines.
Compare Taxi A at $4 plus $2 per mile with Taxi B at $10 plus $1 per mile, then find equal cost.
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Printable 8.EE.C.8c Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.8.EE.C.8c, 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.8a
Interpreting a system’s solution as one point satisfying both equations supports modeling and solving two-equation problems.
- CCSS.Math.Content.8.EE.C.8b
Students must solve the two-variable linear system after translating a problem into equations.
- CCSS.Math.Content.6.EE.C.9
Writing and interpreting one variable relationship with tables and graphs supports modeling a problem as two linear equations.
Keep exploring
Related Standards
- CCSS.Math.Content.7.EE.B
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
- CCSS.Math.Content.8.EE.C.7
Solve linear equations in one variable.
- CCSS.Math.Content.8.EE.C.8
Analyze and solve pairs of simultaneous linear equations.
- CCSS.Math.Content.8.EE.C
Analyze and solve linear equations and pairs of simultaneous linear equations.
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