Maryland Math 8.AT.B.5.b
The Standard
- 8.AT.B.5
- Analyze and solve systems of two linear equations in two variables.
Solve systems of two linear equations by graphing and substitution. When using graphing, find an approximate or exact solution depending on the precision of the graph. Select a method strategically based on the structure of the system or the context of the problem and explain why the method is appropriate.
Maryland College and Career Ready Standards for Mathematics (2025) · MAKE SENSE OF AND SOLVE EQUATIONS, INEQUALITIES, AND SYSTEMS OF EQUATIONS.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find where two lines meet by graphing or substitution. They decide which method fits the equations or the problem, and explain their choice. They tell when a graph gives an estimate rather than an exact answer.
What Mastery Looks Like
- A student solves y = 2x + 1 and x + y = 10 to get (3, 7), then checks the pair in both equations. They can label an intersection on a graph and say whether its coordinates are exact or estimated.
Common Misconceptions
- Students may give only the x-coordinate of an intersection or reverse the coordinates. They may substitute into the same equation they started with instead of the other one. They may treat a rough reading from a graph as exact.
How to Assess It
- Exit ticket: Solve y = 2x + 1 and x + y = 9 by graphing or substitution, and explain your choice. If you graph, say whether your answer is exact or estimated.
Lesson moves
Ways to Teach It
Plot y = 2x + 1 and y = -x + 9 on transparent grids, overlay them, and mark where the lines cross.
Write y = 3x - 2 and 2x + y = 8 on the board; ask partners which method they would choose and why.
Give pairs six system cards with answers on the back; have them sort by method, solve two, and check.
Compare taxi fares of $4 plus $2 per mile and $10 plus $1 per mile; find when the prices match.
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Related Standards
- 8.AT.B.5.a
Interpret the solution to a system of two linear equations as the point where their graphs intersect and verify that the coordinates of the intersection satisfy...
- 6.NOS.C.9
Solve problems in context by graphing points (with the same first coordinate or the same second coordinate) in all four quadrants of the Coordinate Plane.
- 8.AT.B.5.d
Model and solve contextual problems using systems of two linear equations.
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