Graphing Systems of Linear Inequalities

What is one of the main objectives of the lesson?

• To solve quadratic equations

• To graph linear equations

• To check solutions of systems of linear inequalities

• To find the roots of polynomials

What is a system of linear inequalities?

• A set of quadratic inequalities

• A single linear inequality

• A set of equations with no variables

• A set of two or more linear inequalities in the same variables

What does the solution set of a system of linear inequalities represent?

• The area of overlap or intersection of the solutions of all inequalities

• The sum of the solutions of the inequalities

• The union of the solutions of all inequalities

• The difference between the solutions of the inequalities

What must be true for an ordered pair to be a solution to a system of linear inequalities?

• It must be a solution to the first inequality only

• It must satisfy all the inequalities in the system

• It must satisfy at least one of the inequalities

• It must be a solution to the last inequality only

If an ordered pair makes one inequality true but not the other, is it part of the solution set?

• Yes, it is part of the solution set

• No, it must make at least one inequality false

• Yes, if it makes the first inequality true

• No, it must make both inequalities true

What does the dark purple area represent in the graph of a system of linear inequalities?

• The area of the first inequality only

• The solution set of the system

• The area outside the solution set

• The area of the second inequality only

What is the first step in graphing a system of linear inequalities?

• Finding the intersection of the solution areas

• Shading the solution area

• Checking the ordered pairs

• Graphing each inequality in the same coordinate plane

How do you determine the solution set after graphing the inequalities?

• By checking only one inequality

• By shading the entire coordinate plane

• By finding the intersection or overlap of the shaded areas

• By finding the union of the shaded areas

What should you do if there is no overlap in the shaded areas of the graph?

• Shade the entire graph

• Write 'no solution' for the system

• Check the ordered pairs again

• Graph the inequalities again

How can you verify the system of inequalities from a graph?

• By checking a point in the shaded area

• By checking a point at the origin

• By checking a point outside the shaded area

• By checking a point on the boundary line