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Systems of Linear Inequalities

Concept:

A linear inequality in two variables Ax + ByC (or <, >, or ≥) divides the Cartesian coordinate system into two half-planes, one of which is the set of points (x, y) that satisfy the inequality. When there is more than one inequality to be considered at a time, the region where the half-planes overlap is the solution to the system of inequalities.

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 Show intersection
 include x ≥ 0 and y ≥ 0
latus rectum:

eccentricity:

INSTRUCTIONS

EXPLORATIONS

PRACTICE QUESTIONS

1. What plane figure is formed by the individual inequalities 4x + 9y ≥ 36,
9x + 3y ≥ 96, 7x - 4y ≤ -128, and
2x + 9y ≤ -36 when graphed in the same coordinate system?
2. Which point is a solution of the system?
33.6x + 58.8y ≤ 470.4
  13.2x + 6.9y  ≥ -70.2
  9.7x - 16.3y < 22.5
3. The point (8, 12) is a solution of which of the following systems of inequalities?
4. Match the solution set to the system.
17x - 23y ≥ -250
   2x + 3y ≥ 15
,
    x - 10y ≤ -20
       x + y ≤ 20
with x ≥ 0 and y ≥ 0.
5. Which point is NOT a solution of any of these inequalities?
52.6x - 72.9y < 438.2,
67.1x + 47.5y > 231.2, and
6.7x + 28.4y < -343.5

n be any number from to

t can be any number from to