Understanding Systems of Linear Inequalities

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

• Graph each inequality as if it were an equation.

• Shade the entire graph.

• Use only one test point for both inequalities.

• Find the solution algebraically.

How do you determine if a line should be dashed or solid when graphing an inequality?

• By the color of the line.

• By the intercepts of the line.

• By the slope of the line.

• By the inequality symbol used.

What does it mean if a test point results in a false statement when plugged into an inequality?

• The shading should be on the opposite side of the line.

• The inequality is incorrect.

• The test point is on the line.

• The line should be solid.

What is the solution to a system of linear inequalities when graphed?

• The area under the first line.

• The area where the shading of both inequalities overlaps.

• The area where the two lines intersect.

• The area above the second line.

In the second example, how is the x-intercept found for the first inequality?

• By setting y to zero and solving for x.

• By setting x to zero and solving for y.

• By using the slope-intercept form.

• By graphing the inequality directly.

What is the significance of the y-intercept in graphing a line?

• It determines if the line is dashed or solid.

• It is the point where the line crosses the x-axis.

• It is the point where the line crosses the y-axis.

• It determines the slope of the line.

How do you decide which side of the line to shade for an inequality?

• By using a test point.

• By the color of the line.

• By the slope of the line.

• By the intercepts of the line.

What is the slope of the line y = x in the second example?

• 1

• -1

• 0

• Undefined

Why can't the origin be used as a test point for the line y = x?

• Because it is not a valid point.

• Because it is not an integer.

• Because it lies on the line.

• Because it is outside the graph.

What does the overlapping shaded region represent in a system of inequalities?

• The area where no solutions exist.

• The solution to the system of inequalities.

• The area that should not be shaded.

• The solution to only one inequality.