6 6 Solving System of Linear Inequalities Two

6. 6 Solving System of Linear Inequalities: Two or more linear inequality equations. Solution of a System of Linear Equations: Any ordered pair that makes all the equations in a system true.

Always Remember:

GOAL:

Y< x + 1 < : Dashed line and shade below Y> x + 1 > : Dashed line and shade above

Y≤ x + 1 ≤ : Solid line and Shade below ≥ : Solid line and shade above Y≥x+1

Y< x + 1 Y≤ x + 1 Y> x + 1 Y≥x+1

SOLVING A SYSTEM BY GRAPHING: To solve a system of inequalities we must: 1) Write the equations in slope-intercept form (y □ mx+b) 2) Graph the equations and shade 3) Find an ordered pair point inside the shaded intersection region 4) Check

Ex: What is the solution of the system? Use a graph to check your answer. http: //www. meta-calculator. com/online/

SOLUTION: 1) Write the equations in slope-intercept form (y□mx+b)

SOLUTION: 2) Graph the equations Dashed line and shade down Solid line and shade up

SOLUTION: 2) In the same graph:

SOLUTION: 3) Find the solution Looking at the graph, we see that any point in the double shaded region will be a solution, say: (0, 3)

SOLUTION: 4) Check We know that (0, 3) is the solution from our graph.

YOU TRY IT: What is the solution of the system? Use a graph to check your answer.

SOLUTION: 1) Write the equations in slope-intercept form (y=mx+b)

SOLUTION: 2) Graph the equations Dashed line and shade down

SOLUTION: 2) In the same graph:

SOLUTION: 3) Find the solution Looking at the graph, we see that any point in the double shaded region will be a solution, say: (2, -1)

SOLUTION: 4) Check We know that (2, -1) is the solution from our graph.

Real-World: You are planning what to do after school. You can spend at most 6 hrs. daily playing the trumpet and doing homework. You want to spend less than 2 hrs. playing the trumpet. You must spend at least 1. 5 hrs. on homework. What is a graph showing how much you can spend your time?

Real-World(SOLUTION): You are planning what to do after school. You can spend at most 6 hrs. daily playing the trumpet and doing homework. You want to spend less than 2 hrs. playing the trumpet. You must spend at least 1. 5 hrs. on homework. What is a graph showing how much you can spend your time? At most 6 hrs x + y ≤ 6 Less than 2 hrs trumpet x < 2 hrs At least 1. 5 hrs homework y ≥ 1. 5 hrs

SOLUTION: x+y≤ 6 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 y≤-x+6

SOLUTION: x<2 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6

SOLUTION: Y ≥ 1. 5 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6

SOLUTION: All together in the same graph: y≤-x+6 10 x<2 Y ≥ 1. 5 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6

SOLUTION: 10 y≤-x+6 9 8 7 6 5 4 Y ≥ 1. 5 3 2 1 x<2 1 2 3 4 5 6 Any point in the red shaded area are solutions to the problem

YOU TRY IT: You have a job mowing the lawn for $10 per hour. You also have another job playing for parties and you charge $12 per hour. You need to earn at least $350 to buy a new instrument but you cannot work more than 35 hrs per week. You must work a minimum of 10 hrs playing at parties. What is a graph showing how many hours per week you can work at each job?

YOU TRY IT: (SOLUTION) Given info: mowing the lawn X playing at parties y earn at least $350 10 x + 12 y ≥ 350 no more than 35 hrs per week x + y ≤ 35 minimum of 10 hrs playing y ≥ 10

SOLUTION: 10 x + 12 y ≥ 350 60 50 40 30 20 10 10 20 30 40 50 6

SOLUTION: x + y ≤ 35 y ≤ - x + 35 60 50 40 30 20 10 10 20 30 40 50 6

SOLUTION: y ≥ 10 60 50 40 30 20 10 10 20 30 40 50 6

SOLUTION: All in one graph 60 50 y ≤ - x + 35 40 30 20 y ≥ 10 10 10 20 30 40 50 6

SOLUTION: All in one graph 60 50 40 30 y ≤ - x + 35 20 y ≥ 10 10 10 20 30 40 50 6 Any point inside the red region is a solution

VIDEOS: Graphing Inequalities https: //www. khanacademy. org/math/algebra/line ar-equations-and-inequalitie/graphing-linearinequalities/v/graphing-inequalities https: //www. khanacademy. org/math/algebra/line ar-equations-and-inequalitie/graphing-linearinequalities/v/solving-and-graphing-linearinequalities-in-two-variables-1

CLASSWORK: Page 398 -401 Problems: As many as needed to master the concept.