Systems

Solving Systems of Linear Ineqaulities (Shading)

Example:

Graph the system of inequalities: 3x + y __>__ 12 3x + 2y __<__ 15 y __>__ 2

We draw T-tables to graph the two lines. Note that the last two lines is horizontal. 3x + y = 12 3x + 2y = 15
 * ** x ** || ** y ** ||
 * 0 || 12 ||
 * 4 || 0 ||
 * ** x ** || ** y ** ||
 * 0 || 7.5 ||
 * 5 || 0 ||

We solve the two by two system to find the coordinates of the intersection. y = 12 - 3x 3x + 2(12 - 3x) = 15 3x + 24 - 6x = 15 -3x = -9 x = 3 Plugging back in y = 12 - 3(3) = 3

So the point (3,3) is the point of intersection. The graph is shown below.