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7.6 Solving Systems of Linear Inequalities

7.6 Solving Systems of Linear Inequalities. Bell Work:. Check to see if the ordered pairs are a solution of 2x-3y > -2 A. (0,0) B. (0,1) C. (2,-1). Learning Targets:. I can solve a system of linear inequalities by graphing.

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7.6 Solving Systems of Linear Inequalities

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  1. 7.6 Solving Systems of Linear Inequalities

  2. Bell Work: • Check to see if the ordered pairs are a solution of 2x-3y>-2 • A. (0,0) • B. (0,1) • C. (2,-1)

  3. Learning Targets: • I can solve a system of linear inequalities by graphing. • I can use a system of linear inequalities to model a real-life situation.

  4. Remember How to Sketch the graph of 6x + 5y ≥ 30… • Write in slope- intercept form and graph: y ≥ -6/5x + 6 This will be a solid line. • Test a point. (0,0)6(0) + 5(0) ≥ 300 ≥ 30 Not a solution. • Shade the side that doesn’t include (0,0). 6 4 2 -6 -4 -2 2 4 6 8 -2 -4 -6

  5. With a linear system, you will be shading 2 or more inequalities. Where they cross is the solution to ALL inequalities.

  6. y < 2 x > -1 y > x-2 For example… The solution is the intersection of all three inequalities. So (0,0) is a solution but (0,3) is not.

  7. Steps to Graphing Systems of Linear Inequalities • Sketch the line that corresponds to each inequality. • Lightly shade the half plane that is the graph of each linear inequality. (Colored pencils may help you distinguish the different half planes.) • The graph of the system is the intersection of the shaded half planes. (If you used colored pencils, it is the region that has been shaded with EVERY color.)

  8. y < -2x + 2 y < x + 3 y > -x - 1 Practice…

  9. y < 4 y > 1 Practice…

  10. How is the solution of a system of linear inequalities similar to the solution of a system of linear equations?How is it different?

  11. The solution to a system of linear inequalities must satisfy each inequality just as the solution to a system of linear equations must satisfy each equation.The solution to a system of linear inequalities is usually a region, whereas a solution to a system of linear equations is a point or a line.

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