Graphing Systems of Inequalities

Mrs. Petkas guides students through Lesson 6-6, focusing on solving systems of inequalities graphically. The lesson builds on previous knowledge from Lesson 6-5, emphasizing the use of a coordinate plane to graph two inequalities, label them, and identify the solution set through shading. The tutorial includes detailed examples, highlighting the importance of using tools like calculators and rulers for accuracy. Students learn to check solutions by substituting points into the original inequalities, ensuring they satisfy both conditions. The lesson concludes with a word problem, reinforcing the application of these concepts in real-world scenarios.

What tools are recommended to have on hand when solving systems of inequalities graphically?

• Graph paper and pencil

• Protractor and compass

• Calculator and ruler

• Notebook and pen

What is the first step in solving an inequality graphically if it is not already in the correct form?

• Solve for x

• Solve for y

• Plot random points

• Draw a solid line

When graphing an inequality, how do you determine whether to use a dashed or solid line?

• Dashed for 'greater than' and solid for 'less than'

• Dashed for 'less than' and solid for 'greater than'

• Dashed if the inequality does not include 'equal to'

• Solid if the inequality does not include 'equal to'

How many points are recommended to plot for a linear inequality to ensure accuracy?

• At least 5

• At least 3

• At least 2

• At least 4

What should you do if your plotted points for an inequality include decimals or fractions?

• Convert them to percentages

• Plot them as they are

• Skip them and find points with whole numbers

• Round them to the nearest whole number

When shading the region for an inequality, how do you determine which side of the line to shade?

• Shade below for 'greater than' and above for 'less than'

• Shade to the right for 'greater than' and to the left for 'less than'

• Shade above for 'greater than' and below for 'less than'

• Shade to the left for 'greater than' and to the right for 'less than'

What is the purpose of checking a point in the double shaded area of a system of inequalities?

• To determine the slope of the lines

• To find the midpoint of the solution set

• To ensure it satisfies both inequalities

• To verify it lies on the boundary

In the second example, what must you remember to do when dividing by a negative number in an inequality?

• Add the same number to both sides

• Subtract the same number from both sides

• Switch the inequality sign

• Multiply both sides by -1

When solving a word problem involving inequalities, what is the first step?

• Set up the system of inequalities

• Graph the inequalities

• Check a point in the solution set

• Shade the regions

In the word problem, what do the variables x and y represent?

• Dollars and candles

• Candles and dollars

• Large candles and small candles

• Small candles and large candles