Guided Notes on Systems of Inequalities

​Guided Notes on Systems of Inequalities

Multiple Choice

You know that a system of EQUATIONS is...

• two or more equations with the same variables

• Equations related to systems

• Equations where the variable represents the education system

• The formula used by the government to count votes

​•A system of inequalities is when there are _________ or more inequalities on a coordinate plane. 

•There are _________________ solutions to a system of inequalities. 

•These solutions (ordered pairs) can be found in the region where the shaded half-planes __________________.

​two

infinite

overlap

​Steps:

1) Convert to slope-intercept form, if needed (y = mx + b)

2) Graph each boundary line and shade according to inequality sign.

3) Choose a point in the region where the shading overlaps to check.

Remember: If you multiply or divide by a negative, you MUST flip the inequality sign!

Graph the first inequality. Remember to identify the type of line and the shaded region

​Check the next slide to make sure your graph is correct

​How did you do? Answer this question on the next slide.

Poll

How did you do graphing the first inequality?

• Great! Mine looks even better than yours! I am ready to graph the next one.

• Good - I made a minor mistake, but I know what I did wrong.

• Fine, I guess

• I am confused. (if this is you, skip pass the next two slides to watch a video on how to graph this system)

​Graph the other inequality from the system...

​​How did you do?

If you got it, skip the next slide and answer the questions.

If you need more help, see the next slide.

​Watch this video to see how to graph the system if you need a little bit more help.

Draw

Outline or shade the region where the solutions to the system you think are located: (Draw on the screen)

You should have outline / shaded the region where the shaded planes overlap (outlined in yellow to the right)

Multiple Choice

Which of the following ordered pairs is a solution to the system of inequalities we just graphed? - Use your notes!

• (2,-2)

• (5,1)

• (-5,2)

• (-2,1)

​Graph Example 2. Check your work on the next slide.

​Graph Ex. 3 and 4. Check your work on the next slide.

Multiple Choice

Which point is a solution?

• (0, 6)

• (-3, 4)

• (1, 0)

• (-4, 3)

Multiple Choice

Is (0,0) a solution to the system?

• Solution

• Not a solution

Multiple Choice

Is (-2,4) a solution to the system?

• Solution

• Not a solution

Multiple Choice

Match the system to the graph (solution set is on the left)

• y ≤ 3x   and  y ≤ -2x + 4

• y > 3x   and  y > -2x + 4

• y < 3x   and  y > -2x + 3

• y > 3x   and  y < -2x + 4

Multiple Choice

Which system of inequalities matches the graph?

• y > 2x - 4 y < 2

• y < 2x - 4 y < 2

• y > 2x - 4 y <  2 

• y < 2x - 4 y <   -2

Multiple Choice

Which point below is NOT part of the solution set?

• (0, 0)

• (5, 1)

• (-1, -3)

• (20, -5)

Multiple Choice

Which of the following is not a solution to this system of inequalities?

• (0,-1)

• (0,3)

• (4,0)

• (6,-2)

Multiple Choice

Write an inequality represented by the graph.

• x < - 3

• y < - 3

• x > - 3

• x ≥ - 3

Multiple Choice

What is the boundary line (symbol) of the graph?

• less than

• less than or equal to 

• greater than 

• greater than or equal to 

Multiple Choice

This system has an infinite number of solutions, TRUE or FALSE?

• TRUE

• FALSE

Multiple Choice

The graph shows which inequality?

• y ≤ 3
• y ≥ 3
• y > 3
• x > 3

Multiple Choice

Match

• y < x−2 
  y < 3
• y > -x+2
  y > 3
• y < -x+2
  y < 3
• y < -x+2
  y > 3

​Just a Reminder....

​Systems of Inequalities will either have no solutions or infinite solutions.

​When a system of EQUATIONS has parallel lines, there is no solution

​When a system of INEQUALITIES has parallel lines, there could be no solution or infinite solutions