SYSTEMS OF LINEAR INEQUALITIES Solving Linear Systems of
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SYSTEMS OF LINEAR INEQUALITIES Solving Linear Systems of Inequalities by Graphing
Solving Systems of Linear Inequalities We show the solution to a system of linear inequalities by graphing them. a) This process is easier if we put the inequalities into Slope-Intercept Form, y = mx + b. 1.
Solving Systems of Linear Inequalities 2. Graph the line using the yintercept & slope. a) If the inequality is < or >, make the lines dotted. b) If the inequality is < or >, make the lines solid.
Solving Systems of Linear Inequalities 3. The solution also includes points not on the line, so you need to shade the region of the graph: above the line for ‘y >’ or ‘y ’. b) below the line for ‘y <’ or ‘y ≤’. a)
Solving Systems of Linear Inequalities Example: a: b: 3 x + 4 y > - 4 x + 2 y < 2 Put in Slope-Intercept Form:
Solving Systems of Linear Inequalities Example, continued: Graph each line, make dotted or solid and shade the correct area. a: dotted shade above b: dotted shade below
Solving Systems of Linear Inequalities a: 3 x + 4 y > - 4
Solving Systems of Linear Inequalities a: 3 x + 4 y > - 4 b: x + 2 y < 2
Systems of Linear Inequalities n Graph the solution set of the system. The solution set of the system of equations is the region shaded both red and green, including part of the line x + y 3.
Solving Systems of Linear Inequalities a: 3 x + 4 y > - 4 b: x + 2 y < 2 The area between the green arrows is the region of overlap and thus the solution.
nx – 3 y < 6 n 2 x + 3 y > -6 y 10 x -10 10
ny > x 2 – 4 nx+y<2 y 10 x -10 10
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