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Systems of Linear Inequalities definitions

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  • System of Inequalities
    A set of two or more linear inequalities considered together, where the solution is the region satisfying all conditions.
  • Boundary Line
    A straight line on a graph representing the edge of the solution region for a linear inequality.
  • Solid Line
    A continuous line used when the inequality includes equality (≤ or ≥), indicating points on the line are included.
  • Dashed Line
    A broken line used for strict inequalities (< or >), showing points on the line are not part of the solution.
  • Shaded Region
    The area on a graph representing all solutions that satisfy a given inequality.
  • Overlap
    The common area where shaded regions from all inequalities intersect, representing the solution to the system.
  • Test Point
    A coordinate, often (0,0), substituted into an inequality to determine which side of the boundary line to shade.
  • Slope-Intercept Form
    An equation format y = mx + b, making it easy to identify slope and y-intercept for graphing.
  • Inequality Symbol
    A sign such as <, >, ≤, or ≥, indicating the relationship between two expressions.
  • Y-Intercept
    The point where a line crosses the y-axis, used as a starting point for graphing.
  • Slope
    A measure of a line’s steepness, calculated as rise over run between two points.
  • Solution Set
    All coordinate pairs that satisfy every inequality in a system, typically shown as the overlapping shaded region.
  • False Statement
    A result from substituting a test point into an inequality, indicating the point is not in the solution region.
  • No Solution
    A situation where shaded regions do not overlap, meaning no coordinate pair satisfies all inequalities.
  • Graph
    A visual representation on the coordinate plane showing lines and shaded regions for inequalities.