Systems of inequalities

Systems of inequalities

​Title: Solving Systems of Inequalities

Grade level: 8th/9th

Objectives:

• Students will be able to graph systems of inequalities on a coordinate plane.

• Students will be able to identify the solution set for a system of inequalities.

• Students will be able to write a system of inequalities given a verbal description of a real-world situation.

Multiple Choice

-4x + 14 ≤ 54

• x ≥ - 10
• x ≤ -10
• x ≥ 10
• x ≤ 10

Multiple Choice

-8x < 48

• x < -6

• x > -6

• x < 6

• x > 6

Multiple Select

Which of the following are solutions to the inequality $$x>8$$  ?

• 6

• 7

• 9

• 10

Multiple Choice

Warm Up!

After converting from standard form to slope-intercept form, what will the following equation look like?

4x+2y=6  

• y=2x+3

• y=-1/2x-3

• y=-2x+3

• y=-1/2x+3

Fill in the Blank

After converting the following equation from standard form to slope intercept form, what will the following equation be?

3x−6y=12  

(Don't type in any spaces)

Multiple Choice

What is the equation of the graph?

• y>2x+1

• y>1/2x+1

• y<2x+1

• y<1/2x+1

​Graphing Inequalities Reminder

Inequalities involve: >,≥,<,≤

​Steps for graphing inequalities

1. ​Place the equation in slope-intercept form, if necessary

2. ​Graph as if it were a normal linear equation

3. ​Determine if the line is solid or dashed based on inequality

4. ​Shade the appropriate area

5. ​Shade above the line for > or ≥  

6. ​Shade below the line for < or ≤  

   Solving Systems of Inequalities

7. Graph Each Inequality just like we graphed Systems of Equations.

8. The solution is where the inequalities overlap.

Multiple Choice

Solve the system of inequalities by graphing.

Multiple Choice

Solve the system of inequalities by graphing.

Multiple Choice

Match

• y < x−2  y < 3

• y > -x+2 y > 3

• y < -x+2 y < 3

• y < -x+2 y > 3

Determining if an ordered pair is a solution to an inequality.

An ordered pair is a solution to an inequality if it lies in the shaded area or on a solid boundary line.

Ordered pairs that lie on a dashed boundary line are NOT solutions.

Multiple Choice

Which point is a solution?

• (0, 6)

• (-3, 5)

• (1, 0)

• (-4, 3)

Multiple Choice

Which of the following points is a solution to the system of equations below?
x + 2y ≥ 4
3x − 2y < 4
Take your time!

• (0, 0)
• (2, 1)
• (2, 2)
• (-1, 1)

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

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

• Solution
• Not a solution

Multiple Choice

Which point is not a solution?

• (1, 6)

• (-1, 1)

• (3, -2)

• (5, 0)

Multiple Choice

Which point is a solution?

• (0, 6)

• (-3, 5)

• (1, 0)

• (-4, 3)