Eighth Grade · Math · week 14

Systems by graphing

Solve a system of two linear equations by graphing both lines and identifying the intersection point as the solution.

A system of two equations describes two lines. The solution is the one point (x, y) that makes BOTH equations true at once -- where the two lines cross. Build a short table of points for each line, find the point they share, and check it in both equations.

If a shared point is not obvious yet, extend both tables one more step in the same pattern before concluding anything.

📋 For the teacher
Teach it (10–15 min):
  • Frame it plainly: solving a system by graphing means finding the ONE point both lines agree on.
  • Build each line's point table independently first (same skill as graphing a single line) before hunting for the match.
  • Test the crossing point in BOTH original equations -- a point that only satisfies one equation is not the answer.
  • If the tables do not obviously share a point, extend both by one more rise-run step before assuming there is no match yet.
Talk about it:
  • What does the crossing point of two lines actually mean about the two equations?
  • Why do you need to check the solution in BOTH equations, not just one?
  • What would it mean if you extended both tables and never found a matching point?

Mastery looks like: Given two equations, they generate a short point table for each, identify the shared point, and verify it in both equations.

Common stumbles: Stopping after checking the point in only one equation; misaligning the x-values between the two tables so a shared point is missed.

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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