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Two Shadings Overlap

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 44 of 61.

A system of two inequalities shades two half-planes. The solutions of the system are the points where the two shadings overlap. For $y > x-2;\quad y \le -x+4$ , the overlap is the region above the first line and on or below the second line.

$One shading of the pair; the solution is where both hold$

The shading of the first inequality only. The solutions of the system are where both shadings overlap

Each boundary line follows its own sign. Here the first line is dashed and the second is solid. A point solves the system only when it satisfies both inequalities at the same time.

Challenge

Medium

Shade the solutions of the system $y > x-1;\quad y < -x+3$ . Both inequalities must hold.

Try it yourself

y > x-1

y < -x+3

Shade both regions

All lessons in Graphs & Systems

1Points and Rules

Two Numbers, One Point A Rule Makes Points The Points Line Up

4Slope-Intercept Form

y = mx + b The Starting Height Write the Equation Solve for y Draw From Any Form Recap: y = mx + b

7Parallel & Perpendicular

Same Slope, Never Meet The Perpendicular Slope A Right-Angle Line Recap: Two Relations

10Systems by Graphing

Two Lines, One Answer Solve by Drawing Check the Crossing When Lines Never Cross Recap: By Graphing

2The Whole Plane

The Four Quadrants Mirror Points On the Line or Not?Recap: Rule to Line

5Point-Slope Form

A Point and a Slope From Two Points Flat or Vertical Through Draw From a Point Recap: Point-Slope

8Function Notation

The Name of a Rule Inputs With Signs Find the Input The Graph of f Recap: f(x)

11Solving Systems Exactly

Substitution Isolate First Elimination Scale, Then Add Three Unknowns Two Numbers, Two Facts Recap: Two Methods