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Systems of Linear Inequalities definitions

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  • System of Inequalities
    A collection of two or more linear inequalities whose solution is the region where all shaded areas overlap.
  • Boundary Line
    A straight line representing the edge of a linear inequality, drawn solid or dashed based on the inequality symbol.
  • Solid Line
    A boundary drawn when the inequality includes equality, indicating points on the line are part of the solution.
  • Dashed Line
    A boundary drawn when the inequality excludes equality, indicating points on the line are not part of the solution.
  • Slope-Intercept Form
    An equation format y = mx + b, where m is slope and b is y-intercept, used for easy graphing of lines.
  • Y-Intercept
    The point where a line crosses the y-axis, serving as a starting reference for graphing.
  • Slope
    A measure of a line’s steepness, calculated as rise over run, guiding the direction of the graph.
  • Test Point
    A coordinate, often (0,0), used to check which side of a boundary line satisfies the inequality.
  • Shaded Region
    The area on a graph representing all solutions to a linear inequality, determined by test points.
  • Overlap
    The intersection of shaded regions from multiple inequalities, indicating the solution to the system.
  • Solution Region
    The combined area where all inequalities in a system are satisfied simultaneously.
  • Linear Inequality
    An algebraic expression relating variables with inequality symbols, forming a boundary and solution region.
  • Greater Than Symbol
    An inequality sign (>) indicating solutions lie above the boundary line, excluding the line itself.
  • Less Than or Equal Symbol
    An inequality sign (≤) indicating solutions include the boundary line and the area below it.
  • No Solution
    A scenario where shaded regions from all inequalities do not overlap, meaning no common solution exists.