Week 5 — Readings & Resources · Systems of Linear Equations & Inequalities

Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Objective covered: Objective 4 — Graph and analyze linear functions and solve systems of linear equations and inequalities.

How to use this page

Everything here is a link to an external resource — open it in your browser, the same way you'd open a YouTube link. Nothing needs to be downloaded.

This week's load is deliberately light: ~3 readings + ~2 videos, grouped by the four ideas from the lecture. Read or watch one item per group and you're ready for the quiz; do all of them and you'll be very comfortable. Total time is roughly 40–55 minutes if you do everything, far less if you pick one per group.

Reading order that matches the lecture: ① substitution → ② elimination → ③ classifying systems → ④ systems of linear inequalities.

A habit to carry into this week: the AI tutorial ends by having you verify a chatbot's elimination work. Run the algebra yourself first — chatbots frequently make sign errors when multiplying an equation before adding.

① Solving by Substitution & Elimination

Maps to Lecture Segments 2–3. Two methods, one goal: find the (x, y) that satisfies both equations.

Reading — "Systems of Linear Equations: Two Variables" (OpenStax, College Algebra 2e, §7.1)
🔗 https://openstax.org/books/college-algebra-2e/pages/7-1-systems-of-linear-equations-two-variables
Why it's assigned: the clearest single-section treatment of both substitution and elimination — worked examples for both methods with the same problems used in class, plus the geometric interpretation of each outcome.
⏱ ~15 min (focus on the substitution and elimination subsections; skip the applications section for now)

Reading — "Linear Systems with Two Variables" (Paul's Online Math Notes — Algebra, §7.1)
🔗 https://tutorial.math.lamar.edu/classes/alg/SystemsTwoVrble.aspx
Why it's assigned: tight, example-driven treatment of both methods with the same ordering as the lecture — substitution first, elimination second, with explicit attention to the multiply-first step and the sign rules. A great second pass or alternative if OpenStax moves slowly for you.
⏱ ~10 min

② Classifying Systems (Consistent, Inconsistent, Dependent)

Maps to Lecture Segment 4. The three-outcome story: one solution, no solution, infinitely many — and the geometric picture for each.

These are covered in the same §7.1 pages listed above (OpenStax and Paul's both address all three cases in the same reading). The short version to look for:

• One solution (consistent independent): the algebra gives a specific (x, y).
• No solution (inconsistent): the variable cancels and you get a FALSE equation (0 = k, k ≠ 0). Geometrically: parallel lines.
• Infinitely many (dependent): the variable cancels and you get a TRUE equation (0 = 0). Geometrically: same line.

No additional reading required — revisit §7.1 for the classification examples.

③ Systems of Linear Inequalities

Maps to Lecture Segment 5. Shading half-planes, finding the overlap, and testing a point.

Reading — "Graphing Systems of Linear Inequalities" (OpenStax, Intermediate Algebra 2e, §4.7)
🔗 https://openstax.org/books/intermediate-algebra-2e/pages/4-7-graphing-systems-of-linear-inequalities
Why it's assigned: OpenStax College Algebra 2e covers systems of linear inequalities as part of a longer nonlinear chapter; this Intermediate Algebra 2e page presents exactly the two-linear-inequality level we need — boundary lines, half-plane shading, the overlap region, and testing a point. Well-suited to what we did in class.
⏱ ~10 min

④ Video Walkthroughs (choose one)

Maps to all four Lecture Segments. Seeing someone work through the algebra live is especially helpful for elimination.

Video — "Introduction to Systems of Linear Equations" (Professor Leonard)
🔗 https://www.youtube.com/watch?v=jLhMemW5pfI
Why it earns the click: an unhurried, board-based introduction to what a system of equations means, why there are three possible outcomes, and how to read the geometry — ideal as a before-class or after-class orientation.
⏱ ~20–25 min (full lecture — skim to the parts you need)

Video — "Solving Systems of Linear Equations by Substitution" (Professor Leonard)
🔗 https://www.youtube.com/watch?v=awZhi91rA3M
Why it earns the click: step-by-step substitution at the board, with multiple examples and explicit attention to sign handling and back-substitution — the method that trips up the most students when a negative expression is being substituted.
⏱ ~20–25 min (full lecture — focus on the examples)

Optional one-stop references (free online)

If you'd like one optional reference to return to all term, Paul's Online Math Notes — Algebra covers systems in Chapter 7 with notes, examples, and practice problems. Professor Leonard's College Algebra playlist has full-length lectures for every topic in this course.
🔗 Paul's Algebra notes: https://tutorial.math.lamar.edu/classes/alg/alg.aspx
🔗 Professor Leonard — College Algebra / Trigonometry playlist: https://m.youtube.com/playlist?list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP

Pick-one quick path (≈20 min total)

In a hurry? Do exactly these and you'll be ready for the quiz:
1. Read OpenStax §7.1 — Systems of Linear Equations (covers substitution, elimination, and classifying).
2. Read OpenStax Intermediate Algebra §4.7 — Systems of Linear Inequalities (covers graphing and the overlap region).

Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell Prof. Calloway and use the Paul's Online Math Notes reference above in the meantime.