Week 5 — Systems of Linear Equations & Inequalities

Welcome to your Week 5 Start Here page.

Why this matters

Finding the one point where two conditions agree is how a small-business owner learns how many sales cover a setup cost, and how a shopper sees where one phone plan becomes the cheaper choice. Find that point, check it in both equations, and you can trust the decision.

In plain language

Last week every line stood on its own. This week two lines share one graph, and you look for the place where they agree. That place is the solution of a system (the one pair of numbers that makes both equations true at the same time). You will learn two ways to find it with algebra, substitution (swapping one variable for an equal expression) and elimination (adding the equations so one variable cancels). You will also spot the two odd cases, lines that never meet and two copies of one line, and you will shade the region where two inequalities are true together.

• Already covered: Week 2 solved equations; Week 3 read input-output pairs; Week 4 read slopes and intercepts.
• This week: solving a system by substitution and elimination, classifying a system, and shading a system of inequalities.
• How they connect: every system ends as a Week 2 equation, and every graph is a Week 4 line.
• Where we're going next: Week 6, Polynomials & Factoring, starts a new unit.

Focus

Where do two lines meet, and how do you find that point and prove it?

By the end of this module, you should be able to:

• [ ] check an ordered pair in both equations of a system
• [ ] solve a system by substitution or by elimination
• [ ] tell one solution, no solution, and infinitely many apart
• [ ] shade a system of inequalities and use a test point

To-do

Plan your week

1. Read Chapter 5 (about 40 minutes), then the lecture and slides.
2. Work the lecture tutorial (60–90 minutes) and the practice set (about 20 minutes).
3. Do the Model/Build Studio (about 90 minutes), the discussion, and the assignment.
4. Take the quiz.

This week's checkpoint: solve y = 2x and x + y = 9, and check the pair in both equations.

You've got this

Take it in order, and ask your instructor early if a step snags.

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