Graphing Systems of Inequalities

Key Questions

  • How do I graph a linear inequality in two variables?

    A linear inequality is in the form:

    #ax + by > c# or ax + by < c.

    First, graph the line ax + by - c = 0 by the 2 y-intercepts and x-intercepts.

    Then find the area (above or below the line) that make the inequality true. You may use the origin O (0, 0) as test point

    Example. Solve: 2x + 3y > -4

    First, graph the line 2x + 3y + 4 = 0 by the 2 x and y intercepts.
    Make x = 0 -> 3y = -4 -> y = -4/3
    Make y = 0 -> 2x = -4 -> x = -2
    Solve the inequality: f(x) = 2x + 3y + 4 > 0 by using origin O (0, 0) as test point. We get 4 > 0, It is true, then the area above the line is the solution set.
    graph{2x + 3y + 4 = 0 [-10, 10, -5, 5]}

    Nghi N. · 1 · May 29 2015
  • How do I graph a linear inequality in only one variable?

    By linear inequality in one variable, do you mean something like

    #x <= 5#

    or

    #y > 2#

    If yes, just draw your line and shade the entire area that satisfies your inequality

    For example, in #x <= 5#,
    we should draw a vertical line at #x = 5# and shade the entire area to its left (since #<=#)

    For y > 2, we should draw a broken horizontal line (since #>#, not #>=#) at y = 2 and shade the entire area above it

    seph · 1 · Oct 25 2014

Questions

Systems of Inequalities in Two Variables