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Linear Equations and Inequalities - Systems

Linear Equations and Inequalities - Systems
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2015-01-15 04:23
FunctionCoordinate GeometryInequalityGraphing
This example demonstrates the graphical representation and interactive manipulation of systems of linear equations and inequalities. It involves core mathematical concepts such as linear equations, inequalities, function graphs, and coordinate geometry. Construction highlights include commands like Circle, Polygon, Text, Semicircle, Line, Point, Slider, and Locus. Suitable for high school mathematics education to help students visually understand the representation and properties of solution sets for linear equations and inequalities.

GeoGebra Commands & Parameters

  1. Circle(A, 30) → c
  2. Polygon(B, C, D, E) → poly1, b_1, c_1, d, e
  3. Text("Equation 1") → text1
  4. Semicircle(Point[First[inta]], Point[Last[inta]]) → semia1
  5. Semicircle(Point[Last[inta]], Point[First[inta]]) → semia2
  6. Polygon(F, G, H, I) → poly2, f_1, g, h, i
  7. Text("Equation 2") → text2
  8. Semicircle(Point[First[intb]], Point[Last[intb]]) → semib1
  9. Semicircle(Point[Last[intb]], Point[First[intb]]) → semib2
  10. Text("y > " + m1 + "x +" + b1) → text3
  11. Text("y < " + m1 + "x +" + b1) → text4
  12. Text("y ≥ " + m1 + "x +" + b1) → text5
  13. Text("y ≤ " + m1 + "x +" + b1) → text6
  14. Text("y > " + m2 + "x +" + b2) → text8
  15. Text("Eq 1:") → text7
  16. Text("y < " + m2 + "x +" + b2) → text9
  17. Text("y ≥ " + m2 + "x +" + b2) → text10
  18. Text("y ≤ " + m2 + "x +" + b2) → text11
  19. Text("Eq 2:") → text12
  20. Line(S2, S1) → s
  21. Point(s) → K1
  22. Text("y = " + (y(K1)) + (If[y(K1) < t, "<", If[y(K1) > t, ">", "="]]) + m1 + "*" + (x(K1)) + "+" + b1 + " = " + t) → text21
  23. Text("y = " + m1 + "x +" + b1) → text41
  24. Text("y = " + m2 + "x +" + b2) → text42

AI Drawing Prompt Reference

Create a diagram for teaching systems of linear equations and inequalities. Start with a large circle as a background reference. Then construct two polygonal regions representing the solution sets of two equations. Inside each polygon, draw semicircular arcs to mark boundary intersections, and add text labels 'Equation 1' and 'Equation 2'. For each equation, generate six text annotations showing inequality forms (>, <, ≥, ≤) of the linear expression. Finally, draw a straight line across the figure, place a point on it, and display a text comparing the point's y-coordinate with the equation's value. The layout should clearly show the graphical relationships between the two linear equations and their inequalities.
The prompt above was compiled from the original drawing commands and is for reference only.