Systems of Linear Inequalities AII, 2.0: Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices.

Systems of Linear Inequalities Objective Graph, write, and use a system of linear inequalities. – Two Inequalities Why we need this? It will prepare you for college in related fields such as math and science. Key Words System of linear inequalities in two variables – Think about what a system of equations looks like Solution of a system of linear inequalities – Think about shaded regions Graph of a system of linear inequalities – Think about dashed lines, solid lines, and shaded regions

Pre-requisite Check Graph 1)y<-4x 2)x+3y≥3 Check Solutions of Inequalities

You-Try Exercises Graph and test a solution point (ie. (0,0)) ≤ y x 2 + ANSWER

Check whether (3, 1) is a solution of the system of inequalities. – < y2 1y > x y – 2x2x + – ≤ 62y2y > x – 3. 4yx – ≥ 84y4y > 3x3x + ANSWER solution ANSWER not a solution ANSWER not a solution You-Try Exercises

Graphing a System of Linear Inequalities Step 1: – Graph the boundary lines of the inequalities. Use a dashed line for an inequality with. Use a solid line for an inequality with ≤ or ≥. Step 2: – Shade the half-planes for the inequalities. The graph of the system is the region common to all the half- planes.

Graph a System of Two Inequalities Example 1 I DO: Graph the system. 3y – 2x2x < 1y – x ≥ – Inequality 1 Inequality 2 STEP 2Shade the half-plane below y 2x 3 red to represent Inequality 1. = – SOLUTION STEP 1Graph the boundary line of each inequality. Use a dashed line for Inequality 1. Use a solid line for Inequality 2.

Example 1 Shade the half-plane on and above y x 1 blue to represent Inequality 2. Graph a System of Two Inequalities = –– The graph of the system is the overlap, or intersection, of the red and blue regions.

I DO: Graph the system. Checkpoint Graph a System of Two Inequalities 1. y2 < 1y – ≥ ANSWER

WE DO: Graph the system. Checkpoint ANSWER Graph a System of Two Inequalities 2. 3x – > +2y2yx4 ≤

YOU DO: Graph the system. Checkpoint ANSWER Graph a System of Two Inequalities 3. +yx4 > y2x2x3 ≥ –

Conclusion Summary How do you find the solution of a system of linear inequalities? – Graph each inequality. The solution is the overlapping shaded region, if any. Assignment To be completed in class Pg 188 #(10,14,18,24,32)