Week 5 · Readings & resources

Week 5 — Readings & Resources

College Algebra Free sample edition

Your primary reading is Chapter 5 (in this module). Everything below is the optional, go-deeper layer — pick what helps, skip the rest.

How to use this page

This page has 11 items (5 readings and 6 videos). Allow 60–74 minutes for everything. Each group points back to the matching chapter section and class-session segment, so use the full menu when you want more practice, or take the quick path below.

Every video here has captions: turn them on with the CC button in the player. The chapter covers the same ideas in text.

Pick-one quick path (17–20 min total)

① Where do the two lines meet? Substitution and elimination

Chapter 5, Section “Solve by substitution: replace one variable” · Session 1, Segment 2, “Solve by substitution” · Remember: a solution is one ordered pair that makes both equations true, so check it in both.

Systems of Linear Equations — Math is Fun — the gentlest first look, with pictures of two lines crossing, never meeting, or lying on top of each other. This builds on Week 4's work with slope and parallel lines. (reading, 5–8 min)
Ex 1: Solve a System of Equations Using Substitution — Mathispower4u — one complete substitution, from choosing the variable to swap through the final check. (video, 5 min) (captions: creator)
Using the Substitution Method to Solve a System of Equations — Algebra Class — four steps (solve one equation for a variable, substitute, finish the pair, check), then five worked systems, ending with the two special cases: a false leftover such as 4 = −8 means no solution, and a true one such as −12 = −12 means infinitely many. (reading, 6–9 min)
Solving Systems of Equations Using Elimination By Addition — Patrick J — several systems solved by lining up the variables, multiplying one equation when needed, and adding so one variable cancels. Use it while working through the Week-5 module overview. (video, 10 min) (captions: automatic)

② None, one, or infinitely many? Classifying a system and the break-even point

Chapter 5, Section “Classify a system: one, none, or infinitely many” · Session 2, Segment 5, “Classify the system” · Remember: when both variables vanish, a true leftover means infinitely many solutions and a false one means none.

One Solution, No Solution, or Infinitely Many Solutions - Consistent & Inconsistent Systems — The Organic Chemistry Tutor — a run of systems sorted into the three cases, each one tied to what its two lines look like. (video, 7 min) (captions: automatic)
Cost, Revenue, Profit Equations and Break Even Point — Mario's Math Tutoring — how a cost equation and a revenue equation are built from a business story, and how setting them equal finds the break-even point. (video, 4 min) (captions: automatic)

③ Which side gets shaded? Systems of linear inequalities

Chapter 5, Section “Shade a system of linear inequalities” · Session 2, Segment 7, “Systems of linear inequalities” · Remember: a strict sign gets a dashed boundary, and a test point tells you which side to shade.

Graphing Linear Inequalities — Algebra Class — one inequality at a time: a dotted boundary for a strict sign, a solid one when the sign includes equal to, and the test point (0, 0) deciding which side to shade, then a second example rewritten into slope-intercept form first. Stop here before polynomials; next week takes that up. (reading, 6–9 min)
Ex 1: Graph a System of Linear Inequalities — Mathispower4u — one short system graphed boundary by boundary, then the overlap region picked out with a test point. (video, 3 min) (captions: creator)
Graphing Systems of Linear Inequalities - Example 1 — Patrick J — a second worked system, with the choice of dashed or solid lines explained before any shading. (video, 5 min) (captions: automatic)
Systems of Linear Inequalities: Solving by Graphing — Purplemath — worked systems shaded one inequality at a time, with a clear note on reading the region where the shadings overlap. (reading, 6–9 min)

Optional one-stop reference (free online reference)

Linear System of Equations — Wolfram MathWorld — a mathematics encyclopedia's entry on linear systems; read the opening definition of a set of linear equations in shared unknowns, and skip the matrix material that follows, which this course does not cover. (reading, 3–5 min)

Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell your instructor and use the reference above in the meantime.

Provenance: Built with The Course Maker · samples.thecoursemaker.com