Georgia 8.FGR.7.2
The Standard
Show and explain that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because the points of intersection satisfy both equations simultaneously.
Georgia's K-12 Mathematics Standards · Justify and use various strategies to solve systems of linear equations to model and explain realistic phenomena.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students graph two linear equations and identify any shared ordered pair. They verify the pair by substituting its coordinates into both equations and explain why it works for both.
What Mastery Looks Like
- A student accurately graphs each line, names the shared ordered pair, and checks it in both equations. They also recognize parallel lines as no solution and matching lines as infinitely many solutions.
Common Misconceptions
- Students may name the x-intercept or y-intercept instead of the shared point. They may graph with the wrong slope or reverse the coordinates. Some assume a crossing point is correct without checking it in both equations.
How to Assess It
- Give an exit ticket with y = 2x + 1 and y = -x + 7. Ask students to graph, circle the shared point, and verify it by substitution.
Lesson moves
Ways to Teach It
Graph one equation on each sheet of tracing paper, overlay the sheets, and mark the ordered pair where the lines cross.
Write two sentences explaining why a crossing point must make both equations true, using its x and y coordinates as evidence.
In pairs, draw two equation cards, graph them on mini whiteboards, and earn a point after checking the intersection by substitution.
Model two taxi fares, $4 plus $2 per mile and $10 plus $1 per mile, then find when the costs match.
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Related Standards
- 8.PAR.4.2
Show and explain that the graph of an equation representing an applicable situation in two variables is the set of all its solutions plotted in the coordinate p...
- 8.FGR.7.4
Analyze and solve systems of two linear equations in two variables algebraically to find exact solutions.
- 8.FGR.7.3
Approximate solutions of two linear equations in two variables by graphing the equations and solving simple cases by inspection
- 8.FGR.7.1
Interpret and solve relevant mathematical problems leading to two linear equations in two variables.
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