Question 1

Which of the following ordered pairs is a solution to the inequality $$4x - 2y \geq 8$$?

Accepted Answer

$$(4, 2)$$

Question 2

When graphing the inequality $$y \u003c 3$$, which of the following describes the correct graph?

Accepted Answer

A dashed horizontal line at $$y = 3$$ with shading below the line.

Question 3

Which of the following best describes the solution set for the system of inequalities $$y \u003e 2$$ and $$x \u003c 1$$?

Accepted Answer

The region above $$y = 2$$ and to the left of $$x = 1.$$

Question 4

A company produces two products, A and B. The company can make at most 100 units of A and at most 80 units of B per week. Which system of inequalities models this situation?

Accepted Answer

$$x \leq 100,\ y \leq 80$$

Question 5

Which of the following is the correct first step to graph the inequality $$2x + 3y \u003c 6$$?

Accepted Answer

Graph $$2x + 3y = 6 as a $$dashed line.

Question 6

If the solution to a system of inequalities is the region above $$y = 1$$ and to the right of $$x = -2$$, which system is represented?

Accepted Answer

$$y \u003e 1,\ x \u003e -2$$

Question 7

Which test point is most commonly used to determine which half-plane to shade when graphing a linear inequality, provided the boundary does not pass through it?

Accepted Answer

$$(0, 0)$$

Question 8

A region is shaded above the line $$y = -x + 4$$ and to the left of the line $$x = 3. $$Which system of inequalities describes this region?

Accepted Answer

$$y \u003e -x + 4,\ x \u003c 3$$

Question 9

Which of the following statements is true about the graph of the inequality $$x \geq 2$$?

Accepted Answer

It is a solid vertical line at $$x = 2$$ with shading to the right.

Question 10

Which of the following points is NOT a solution to the system $$y \u003e 1$$ and $$x \u003c -2$$?

Accepted Answer

$$(-2, 3)$$

Question 11

A circular region is defined by the inequality $$x^2$$ + $$y^2$$ \u003c 9$$. Which of the following best describes the solution set?

Accepted Answer

All points inside the circle of radius 3 centered at the origin.

Question 12

Which of the following is the correct way to graph the inequality $$x \u003e 1$$?

Accepted Answer

Draw a dashed vertical line at $$x = 1$$ and shade to the right.

Question 13

A system of inequalities is given by $$y \leq 2x + 1$$ and $$y \u003e -x + 4. $$Which of the following points is in the solution set?

Accepted Answer

$$(1, 3)$$

Question 14

Which of the following best describes the solution set for the system $$y \geq 1$$ and $$y \u003c 4$$?

Accepted Answer

The region between and including $$y = 1$$ and $$y = 4$$, but not including $$y = 4.$$

Question 15

A real-world scenario: A nutritionist recommends that a patient consume at least 50 grams of protein and no more than 70 grams of fat per day. Let $$x be $$grams of protein and $$y be $$grams of fat. Which system of inequalities models this recommendation?

Accepted Answer

$$x \geq 50,\ y \leq 70$$

Question 16

Which of the following is true about the solution set of a system of linear inequalities?

Accepted Answer

It is the intersection of the solution sets of each individual inequality.

Question 17

If you graph the inequality $$y \leq -2x + 5$$, which of the following is true?

Accepted Answer

The boundary is a solid line and the region below the line is shaded.

Question 18

A system of inequalities is given by $$x \u003e 0$$ and $$y \u003c 0. $$Which quadrant contains the solution set?

Accepted Answer

Quadrant IV

Question 19

Which of the following is the correct interpretation of the shaded region for the inequality $$y \geq 2$$?

Accepted Answer

All points on and above the horizontal line $$y = 2.$$

Systems of Inequalities in Two Variables

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