SYSTEMS OF LINEAR INEQUALITIES LINEAR INEQUALITY A Linear

SYSTEMS OF LINEAR INEQUALITIES

LINEAR INEQUALITY A Linear Inequality involves a linear expression in two variables by using any of the relational symbols such as <, >, ≤ or ≥

EXAMPLES: x≥ 4 x-y>4 x+y≤ 3 y < -2

SOLUTION TO A SYSTEM OF INEQUALITY An ordered pair (x, y) is a solution of an inequality in two variables if a true statement results when the variables in the inequality are replaced by the coordinates of the ordered pair.

EXAMPLES: � Determine whether the given ordered pair is a solution to the linear inequality. x - y > 4; (7, 2) 7 – 2 > 4 5 > 4 x + y ≤ 3; (4, 5) 4 + 5 ≤ 3 9 ≤ 3

GOOD TO KNOW: �A linear inequality divides a plane into two parts. �If the boundary line is solid, then the linear inequality must be either ≥ or ≤. �If the boundary line is dotted, then the linear inequality must be either > or <.

Graph the linear inequality. 8 y ≤ 3 x - 2 6 4 2 -8 -6 Solid boundary lines tell that the points on the line are part of the solution set. -4 -2 -2 2 4 6 8 -4 -6 -8 The half plane consists of the points whose coordinates satisfy the inequality.

Graph the linear inequality. 8 y < 3 x - 2 6 4 2 -8 -6 -4 -2 -2 2 4 6 8 -4 -6 -8 Broken boundary lines tell that the points on the line are not part of the solution set.

Graph the linear inequality. y≥ 0 8 6 4 2 -8 -6 -4 -2 -2 -4 -6 -8 2 4 6 8

Graph the linear inequality. x>2 8 6 4 2 -8 -6 -4 -2 -2 -4 -6 -8 2 4 6 8

EXERCISES Do page 52 numbers 914 on your notebook.

Where do you stand? What can you do to make things equal?

SYSTEM OF LINEAR INEQUALITY Two or more linear inequalities considered together

Graph the system. 8 6 4 2 -8 -6 -4 -2 -2 -4 -6 -8 2 4 6 8

Graph the system. 8 6 4 2 -8 -6 -4 -2 -2 2 4 6 8 -4 -6 -8 The region shaded when the inequalities are graphed consists of points that satisfy the system of inequalities.

Graph the system. 8 6 4 2 -8 -6 -4 -2 -2 -4 -6 -8 2 4 6 8

Graph the system. 8 6 4 2 -8 -6 -4 -2 -2 -4 -6 -8 2 4 6 8

Graph the system. 1) 8 6 4 2 -8 -6 -4 -2 -2 -4 -6 -8 2 4 6 8

Write the system of inequalities graphed below. 8 6 x<3 4 2 y < 2 x + 6 -8 -6 -4 -2 -2 -4 -6 -8 2 4 6 8

Graph the linear inequality. 8 6 4 2 -8 -6 -4 -2 -2 -4 -6 -8 2 4 6 8

Graph the linear inequality. 8 6 4 2 -8 -6 -4 -2 -2 -4 -6 -8 2 4 6 8

Graph the linear inequality. 8 6 4 2 -8 -6 -4 -2 -2 -4 -6 -8 2 4 6 8

Graph the linear inequality. 8 6 4 2 -8 -6 -4 -2 -2 -4 -6 -8 2 4 6 8

EXERCISES Page 52 numbers 15 - 19

HOMEWORK Answer the exercises on pages 52 – 53 of the textbook nos. 20 – 28 (even nos. only) on a graphing paper.