Systems of Linear Inequalities
I can graph a system of linear inequalities and find the region where both are true.
What students learn
Students learn to graph two inequalities on one grid, find the overlap where both are true, and test a point in both inequalities.
See inside
The key rule
Graph each inequality on one grid. The solutions are the overlap: the points that make both true.
true and true → solution
One false test is enough: a point in only one shaded region is not a solution.
Watch out
Is (4, 1) a solution of y ≤ x + 2 and x + y < 4?
The mistake: 1 ≤ 4 + 2 is true, so yesIt was checked in only one inequality.
The fix: x + y < 4: 4 + 1 < 4 is false, so noA solution must make both true; (4, 1) fails x + y < 4.
The mistakes it targets
- Checks a point in only one inequality
- Reads a solid boundary as dashed, or a dashed one as solid
- Counts a point on a dashed boundary as a solution
- Shades every region either inequality covers instead of the overlap
The interactive Teacher Deck (32 slides, PowerPoint)
- The Learn page taught on screen: 8 fill-in blanks, each filled on its own click as students write it
- The worked example one slide per step (four steps), each with the reason for the step
- Six practice and three apply problems: a your-turn slide with a think-time bar, then the solution one line per click
- Jump buttons on every slide: go straight to any problem, the answer bank or the exit ticket
- Speaker notes on each problem: the question to ask, the worked answer and the common error to listen for
- A completed deck PDF (19 pages) with every slide fully built, to print or post
The student packet (9 pages)
- Learn: guided notes with four definitions, the key rule, a worked example and a Watch Out error pair
- Practice: two warm-up, two standard and two stretch problems, with an answer bank for self-checking that hides three common-mistake decoys
- Apply: one word problem, a reasoning prompt and one error analysis
- Assess: an exit ticket of four items, two per page, with an I-can self-rating
- Homework (page 5): eight new problems, two warm-up, four standard and two stretch
- Answer key (pages 6–7): every problem worked step by step, four common mistakes with what to do about each, and a grading guide, plus the homework key (page 8)
- Color and ink-saver editions of the whole packet
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.