Systems of Inequalities

What type of line is used for inequalities with '<' or '>'?

• A solid line is used for inequalities with '<' or '>.'

• A dotted line is used for inequalities with '<' or '>.'

• A dashed line is used for inequalities with '<' or '>.'

• A thick line is used for inequalities with '<' or '>.

What type of line is used for inequalities with '≤' or '≥'?

• A dashed line

• A solid line

• A dotted line

• A broken line

What is a system of inequalities?

• A set of two or more inequalities with the same variables, where the solution is the region where the graphs overlap.

• A single inequality that describes a linear relationship between two variables.

• A collection of equations that have no solutions.

• A method for solving quadratic equations.

What does the inequality 'y > 3' represent graphically?

• It represents all points below the horizontal line y = 3, including the line itself.

• It represents all points above the horizontal line y = 3, including the line itself.

• It represents all points above the horizontal line y = 3, not including the line itself.

• It represents all points on the horizontal line y = 3 only.

What is the first step in graphing the inequality 'y < 2x + 1'?

• First, graph the line y = 2x + 1 using a dotted line since the inequality is '<'.

• First, graph the line y = 2x + 1 using a solid line since the inequality is '<'.

• First, find the x-intercept of the line y = 2x + 1.

• First, shade the area above the line y = 2x + 1.

What does the inequality 'x ≥ 3' represent graphically?

• It represents all points to the left of the vertical line x = 3, excluding the line itself.

• It represents all points to the right of the vertical line x = 3, including the line itself.

• It represents all points on the vertical line x = 3 only.

• It represents all points below the horizontal line y = 3.

How do you represent a solution to a system of inequalities graphically?

• By plotting the points of each inequality separately.

• By shading the region where the graphs of the inequalities overlap.

• By drawing a single line that represents all inequalities.

• By listing the solutions in a table format.

How do you solve a system of inequalities by graphing?

• 1. Graph each inequality on the same coordinate plane, then find the intersection of the lines.

• 2. Graph each inequality on the same coordinate plane. Shade the appropriate region for each inequality. The solution is where the shaded regions overlap.

• 3. Solve each inequality separately and then combine the solutions into one.

• 4. Graph the inequalities on separate planes and find the maximum and minimum values.

What is the significance of the intersection of two inequalities?

• It represents the set of points that satisfy both inequalities simultaneously.

• It shows the maximum value of the inequalities.

• It indicates the area where one inequality is greater than the other.

• It provides the average of the two inequalities.

What does the symbol '<' indicate in an inequality?

• The symbol '<' indicates that the value on the left is greater than the value on the right.

• The symbol '<' indicates that the value on the left is equal to the value on the right.

• The symbol '<' indicates that the value on the left is less than the value on the right.

• The symbol '<' indicates that the value on the left is not equal to the value on the right.