Lesson 2: Graphing System of Linear Inequalities

Question 1

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

Answer 1

Solve each inequality for y (if necessary) to put it in slope-intercept form (y = mx + b).

Question 2

What is the second step in solving a system of linear inequalities?

Answer 2

Graph each inequality on the same coordinate plane:
• Use a solid line for ≤ or ≥ inequalities.
• Use a dashed line for < or > inequalities.

Question 3

What is the third step in solving a system of linear inequalities?

Answer 3

Shade the region of the graph that satisfies each inequality:
• Above the line for > or ≥ inequalities.
• Below the line for < or ≤ inequalities.

Question 4

What is the fourth step in solving a system of linear inequalities?

Answer 4

Identify the region where the shaded areas overlap; this overlapping region represents the solution set to the system.

Question 5

T F

If the symbol of inequality is ≥ or ≤, then the graph of a linear inequality is a solid line.

Answer 5

True – For inequalities with ≥ or ≤, the boundary line is solid.

Question 6

T F

The solution of a system of linear inequalities is the set of points or ordered pairs that satisfy all inequalities in the system.

Answer 6

True – The solution set is where the shaded regions of all inequalities overlap.

Question 7

T F

The system of inequalities has no solution if the shaded regions of each inequality do not overlap.

Answer 7

True – If there is no overlapping region, there is no solution to the system.

Question 8

T F

The solution to a system of two linear inequalities can be a single point.

Answer 8

False – The solution set is typically a region, not a single point.

Question 9

T F

The solution set of a system of two linear inequalities is the region where the graphs of the inequalities intersect.

Answer 9

True – The overlapping area represents all solutions satisfying both inequalities.