Understanding Solutions to Systems of Linear Inequalities

The video tutorial explains how to determine if ordered pairs are solutions to a system of linear inequalities. It involves substituting the pairs into the inequalities and checking if both are satisfied. The first pair fails to satisfy both inequalities, while the second pair does. The results are verified graphically, showing the solution lies in the double shaded region.

What must an ordered pair satisfy to be considered a solution to a system of linear inequalities?

• Neither inequality

• Any one inequality of choice

• Only one of the inequalities

• Both inequalities

What is the result of substituting the ordered pair (2, -2) into the inequality x - 3y ≥ 4?

• The inequality is equal to zero

• The inequality is undefined

• The inequality is true

• The inequality is false

After substituting (2, -2) into the inequality 2x - y < 1, what conclusion can be drawn?

• The ordered pair satisfies the inequality

• The ordered pair does not satisfy the inequality

• The ordered pair is a solution to the system

• The ordered pair is irrelevant

What is the simplified form of the expression after substituting (-3, -4) into the inequality x - 3y ≥ 4?

• 0 ≥ 4

• 5 ≥ 4

• 9 ≥ 4

• 3 ≥ 4

What is the result of substituting (-3, -4) into the inequality 2x - y < 1?

• The inequality is undefined

• The inequality is false

• The inequality is true

• The inequality is equal to zero

Which ordered pair is a solution to the system of inequalities?

• (1, 1)

• (0, 0)

• (-3, -4)

• (2, -2)

What does the double shaded region in the graph represent?

• The area where neither inequality is satisfied

• The area outside the solution set

• The area where only one inequality is satisfied

• The area where both inequalities are satisfied

Which point is not in the double shaded region of the graph?

• (-3, -4)

• (2, -2)

• (0, 0)

• (1, 1)

What is the significance of the point (-3, -4) in the graph?

• It is irrelevant to the system

• It lies outside the graph

• It is a solution to the system

• It is not a solution to the system

What conclusion can be drawn about the point (2, -2) based on the graph?

• It lies in the double shaded region

• It is a solution to the system

• It satisfies both inequalities

• It is not a solution to the system