Q: Which of the following best describes the solution set of the system of inequalities $y > 2x + 1$ and $y < -x + 4$?

The region between the two lines.

Q: A company must satisfy the constraints $5x + 6y < -30$ and $2x + 3y \geq -4$. Which region represents the solution set?

The region where both inequalities overlap.

Q: Which of the following statements about the intersection of two solution sets is correct?

It includes only points that satisfy both inequalities.

Q: When graphing $x \geq 3$, what type of line and shading should be used?

Solid line at $x = 3$, shade to the right

Q: If a solution set is defined by $y > 2x + 1$ or $y < -x + 4$, what does the solution set represent?

The region outside the area between the two lines.

Q: Which of the following is NOT a correct step when solving a linear inequality in two variables?

Shade the region that does not satisfy the inequality.

Question 1

Which of the following best describes the solution set of the system of inequalities $y > 2x + 1$ and $y < -x + 4$?

Accepted Answer

The region between the two lines.

Question 2

Given the inequality $2y - 4x < 16$, which of the following points is in the solution set?

Accepted Answer

$(0, 0)$

Question 3

When graphing the inequality $y \leq 3$, what type of boundary line should be used?

Accepted Answer

A solid line at $y = 3$

Question 4

Which of the following best describes the solution set for $x > 2$?

Accepted Answer

All points to the right of $x = 2$

Question 5

A company must satisfy the constraints $5x + 6y < -30$ and $2x + 3y \geq -4$. Which region represents the solution set?

Accepted Answer

The region where both inequalities overlap.

Question 6

If the boundary line for an inequality is $y = -x + 2$ and the inequality is $y > -x + 2$, which side of the line should be shaded?

Accepted Answer

Above the line

Question 7

Which of the following is the correct first step to graph the inequality $2y - 4x < 16$?

Accepted Answer

Rewrite as $y < 2x + 8$

Question 8

Which of the following statements about the intersection of two solution sets is correct?

Accepted Answer

It includes only points that satisfy both inequalities.

Question 9

If you are given the system $y \leq 3$ and $x > -1$, which region should be shaded?

Accepted Answer

Below $y = 3$ and to the right of $x = -1$

Question 10

Which of the following best describes the union of two solution sets?

Accepted Answer

The set of points that satisfy at least one inequality.

Question 11

A region is defined by $y < -1$. Which of the following points is in the solution set?

Accepted Answer

$(2, -2)$

Question 12

When graphing $x \geq 3$, what type of line and shading should be used?

Accepted Answer

Solid line at $x = 3$, shade to the right

Question 13

Which of the following is a correct test point for the inequality $y < 2x + 5$ if the boundary line is $y = 2x + 5$?

Accepted Answer

$(0, 0)$

Question 14

If a solution set is defined by $y > 2x + 1$ or $y < -x + 4$, what does the solution set represent?

Accepted Answer

The region outside the area between the two lines.

Question 15

Which of the following is NOT a correct step when solving a linear inequality in two variables?

Accepted Answer

Shade the region that does not satisfy the inequality.

Question 16

If the inequality is $y \geq 2x - 3$, which of the following points is NOT in the solution set?

Accepted Answer

$(1, -5)$

Question 17

Which of the following best describes the meaning of the symbol $\cap$ when joining solution sets?

Accepted Answer

Intersection

Question 18

A region is defined by $x \leq 2$ and $y > -1$. Which of the following points is in the solution set?

Accepted Answer

$(2, 0)$

Question 19

Which of the following is the correct interpretation of the solution set for $y \leq 3$?

Accepted Answer

All points below and on the line $y = 3$

Question 20

If the solution set is the union of $A$ and $B$, which of the following is true?

Accepted Answer

It contains all points in $A$ or $B$.

Systems of Linear Inequalities in Two Variables

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