NY Next Generation Math NY-8.EE.8.a
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. Recognize when the system has one solution, no solution, or infinitely many solutions.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students understand that a system's solutions are graph intersection points because those coordinates satisfy both equations. They recognize systems with one solution, no solution, or infinitely many solutions.
What Mastery Looks Like
- A student identifies (2, 3) as the intersection of two lines and verifies it in both equations. The student explains that parallel distinct lines have no solution and the same line has infinitely many solutions.
Common Misconceptions
- Students may report an intercept from one line as the system solution or read an intersection inaccurately. They may label parallel lines as one solution or coincident lines as no solution.
How to Assess It
- Show graphs of three systems representing the three solution counts. Ask students to classify each and verify the visible intersection when there is one.
Lesson moves
Ways to Teach It
Graph equation pairs on transparent grids, overlay the lines, and test any shared point in both equations.
Ask students why two different parallel lines cannot share an ordered-pair solution.
Play solution-count sort with equation pairs, line graphs, intersection descriptions, and verification statements.
Interpret intersections or nonintersections of two cost or distance relationships in context.
Keep exploring
Related Standards
- NY-8.EE.8.c
Solve real-world and mathematical problems involving systems of two linear equations in two variables with integer coefficients.
- NY-8.EE.8.b
Solve systems of two linear equations in two variables with integer coefficients: graphically, numerically using a table, and algebraically. Solve simple cases ...
- NY-8.EE.7.a
Recognize when linear equations in one variable have one solution, infinitely many solutions, or no solutions. Give examples and show which of these possibiliti...
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