System of Linear Inequalities in Two Variables

Which of the following represents a system of linear inequalities in two variables?

• x + y ≤ 5

• 3x + 2y=10

• 2x − 3y > 7

• y ≥ 2x + 3

How many solutions can a system of linear inequalities have?

• One solution

• Infinite solutions

• Two solutions

• No solution

If the solution to system of linear inequalities is a shaded region in a graph, what does this shaded region represent?

• The possible values that satisfy both inequalities

• The x-intercepts of the inequalities

• The impossible values that satisfy both inequalities

• The y-intercepts of the inequalities

Which method can be used to solve a system of linear inequalities?

• Substitution

• Graphing

• Elimination

• All of the above

What does it mean if a point lies on the boundary line of a system of linear inequalities?

• It is a solution to the system

• It is part of the feasible region

• It is not a solution to the system

• It is an invalid point

Which of the following represents a system of linear inequalities with no solution?

• x + y ≥ 5 and x + y ≤ 3

• 3x + 2y ≥ 10 and 3x + 2y ≤ 5

• 2x−3y > 7 and 4x−6y > 14

• y ≤ 2x+3 and y > 2x+3

How can you determine if a point is a solution to a system of linear inequalities?

• Plug the point into both inequalities and see if they are true

• Check if the point is on the x-axis

• Only plug the point into one of the inequalities

• Check if the point is on the y-axis

What is the solution to the system of linear inequalities: y ≥ −2x+4 and y ≤ 3x+1 ?

• (−1,6)

• (0,4)

• (2,5)

• (3,7)

Which of the following represents the feasible region of a system of linear inequalities?

• The x-intercepts of the inequalities

• The region outside the shaded area

• The region inside the shaded area

• The y-intercepts of the inequalities

When solving a linear inequalities algebraically, what does it mean if you arrive at a FALSE statement like 0 > 5 ?

• The system has no solution

• The system has exactly one solution

• The system has infinite solutions

• The system cannot be solved algebraically