Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Module: Week 5 of 16 · Fall 2026 · in-person, two 75-minute sessions
Objective covered: Objective 4 — Graph and analyze linear functions and solve systems of linear equations and inequalities.

This file holds two pieces: (A) the Module 5 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. Dates below assume a Tuesday/Thursday session pattern with Week 5 meeting Tue Sep 29 and Thu Oct 1, and end-of-week work due Sunday Oct 4, 11:59 p.m. Adjust the day-of-week and times to match your section.

(A) Module 5 Overview — Start Here

Welcome to Week 5: Systems of Linear Equations & Inequalities

This is your home base for the week. Read it first, then work the checklist below from top to bottom. Everything you need is linked inside the module.

Last week you mastered the single line — its slope, its equation, its graph. This week the question changes: what happens when two lines share the same xy-plane? They either cross once, run side by side forever, or are secretly the same line. Each case has a name and a meaning, and College Algebra gives you two clean methods — substitution and elimination — to sort them out every time.

The week's big question

"When two linear equations describe the same world, how do we find the point — if there is one — where both are true at once?"

By Sunday you'll solve any 2×2 linear system by substitution and by elimination, classify a system as consistent independent, inconsistent, or dependent at a glance, and sketch the region that satisfies a system of linear inequalities.

By the end of this week, you can…

Use this as a checklist. If you can do all four, you're ready for the quiz.

• [ ] Solve a 2×2 linear system by substitution — isolate one variable in one equation, substitute into the other, solve, and back-substitute for the second value.
• [ ] Solve a 2×2 linear system by elimination — multiply one or both equations so a variable cancels, add the equations, and solve.
• [ ] Classify a system as consistent independent (one solution, lines intersect), inconsistent (no solution, parallel lines), or dependent (infinitely many solutions, same line) — and explain the geometric picture for each.
• [ ] Graph and interpret a system of linear inequalities — shade each half-plane, identify the overlapping region as the solution set, and test a point to verify.

What's due this week, and when

Work these in order — each one gets you ready for the next.

Heads-up on AI and systems: chatbots often make sign errors when eliminating — adding instead of subtracting, or forgetting to multiply every term. Run the algebra yourself first, then ask the chatbot to check. Catching the model is the point.

Late policy reminder: 10% off per day late. If life happens, reach out before the deadline.

How to succeed this week

• Pick your method deliberately. Substitution wins when one equation already has a variable isolated (like y = 2x). Elimination wins when the coefficients line up nicely for cancellation. Having both tools matters.
• Always back-substitute and check. After you find x, plug it back in to get y — then plug both into the other original equation to verify. Two-step checking eliminates almost all errors.
• Memorize the three pictures. Intersecting lines → one solution. Parallel lines → no solution (the variable cancels and you get a false equation like 0 = 7). Same line → infinitely many (the variable cancels and you get a true equation like 0 = 0).
• For inequalities: test a point. After shading two half-planes, pick a point that looks like it's inside the overlap and plug it into both inequalities. If both are satisfied, you've got the right region.
• Show every step. Elimination especially tempts you to skip the "multiply the equation" step — write it down, or you'll lose a sign.

Two lines, two equations, one intersection. That's the geometry; the algebra is just the way we find it exactly. See you Tuesday.

(B) Welcome Announcement — Module 5

Release setting: post on the module's start day (offset = 0 days), i.e., Mon Sep 28, 2026 — not before. If your platform won't preserve the scheduled date on import, post this as a draft labeled "Release: Mon Sep 28."

Subject: Week 5 — when two equations meet 👋

Hi everyone,

Quick scenario: you're running a small event. Adult tickets cost $8, child tickets cost $5, and you sold 10 tickets total for $68. How many of each? That's not a trick question — it's a system of two equations in two unknowns, and this week you'll solve it in under two minutes.

Week 5 — Systems of Linear Equations & Inequalities — the big question is: When two lines share the same world, where do they agree? You'll leave this week with two methods (substitution and elimination), the ability to classify a system by its geometry (one solution, none, or infinitely many), and a feel for the overlapping region when two inequalities run at the same time.

Three things not to miss:
1. Lecture Tutorial 5 — work through all four topics with one approved chatbot (Gemini, Claude, or ChatGPT) and submit the share link. Chatbots tend to make sign errors in elimination — catching that is the point. Due Sun Oct 4.
2. Quiz 5 (no AI) and Discussion 5 — "Substitution or Elimination?" also close Sun Oct 4 — start the discussion early so you have time to reply to two classmates.
3. Assignment 5 — four AI-coached problems with a self-scored report; due Sun Oct 4.

One promise: every system in this course reduces to either "pick a method, solve cleanly, and check" — or "recognize the pattern and call it inconsistent/dependent." The checking step is what separates a strong solver from a lucky one.

Open the Start Here / Module Overview page first. See you Tuesday.

See you soon,
Prof. Calloway