Use graphing to solve this system. 1. y = 2x y = -x + 3 Use substitution to solve this system. 2. y = x-2 -2x -4y = 4 Use elimination to solve this system of equations. 3. 3x – 4y = 3 -3x - 2y = -9 Graph each linear inequality. 4.-4x + 2y < 6 5. y > x -3

Lesson 3.4 Systems of Linear Inequalities

A system of linear inequalities is a collection of linear inequalities in the same variables. The solution of a system of linear inequalities is any ordered pair that satisfies each of the inequalities in the system.

GRAPH the system of linear inequalities. y < x + 2 y ≥ -2 Steps: Graph the lines Use a solid line for ≤ or ≥ and a dotted Line for > or < Substitute (0,0) in each inequality. If true, shade the side that contains The point (0,0). If false, shade the opposite side. The solution is ALL the ordered pairs in the intersection of the two shaded regions.

Example #2 y ≥ -x -1 y≤ 2x + 1 X < 1

#1 -5< y < 1 #2 -3 < x < 4

#1 #2

 A teacher works for a textbook company during the summer. He makes $35 per page to write the material and $25 per page to type it. The teacher would like to earn at least $3500, but does not want more than 120 pages of work. Let x be the number of pages written and y be the number of pages typed. Write a system of inequalities to represent this situation.  x + y ≤ 120  35x + 25y ≥ 3500

Lesson 3.4 Page 183 (10-24 EVENS, EVENS, 48a, 51a