Systems Test Study Guide

Which point below is NOT part of the solution set?

• (0, -2)

• (1, 1)

• (3, 3)

• (2, 10)

Answer explanation

The point (3, 3) does not satisfy the equation or condition defined by the solution set, making it the only point that is not part of the solution. The other points (0, -2), (1, 1), and (2, 10) are valid solutions.

Which point below is NOT part of the solution set?

• (3, 4)

• (0, 4)

• (-2, 6)

• (6, 2)

Answer explanation

The point (0, 4) does not satisfy the conditions of the solution set, while (3, 4), (-2, 6), and (6, 2) do. Therefore, (0, 4) is the correct answer as it is NOT part of the solution set.

Tags

CCSS.HSA.REI.D.12

Is (-1, 0) a solution to this inequality?

• Yes

• No

Answer explanation

To determine if (-1, 0) is a solution, substitute -1 for x and 0 for y in the inequality. If the inequality does not hold true, then (-1, 0) is not a solution. Thus, the correct answer is No.

Is (1, 6) a solution to this inequality?

• Yes

• No

Answer explanation

To determine if (1, 6) is a solution, substitute x=1 and y=6 into the inequality. If the inequality holds true, then (1, 6) is a solution. Since it satisfies the inequality, the answer is Yes.

Are the points on the boundary line part of the solution set or not?

• Yes, they are part of the solution set

• No, they are NOT part of the solution set

Answer explanation

Yes, the points on the boundary line are part of the solution set when the inequality is inclusive (e.g., ≤ or ≥). This means that the boundary points satisfy the equation and are included in the solution.

Tags

CCSS.HSA.REI.D.12

Which of the following ordered pairs is a solution of the inequality 3x + 2y > 1?

• ( -1, -5 )

• ( -5, 4 )

• ( -6, 0 )

• ( 2, 4 )

Answer explanation

To check which pair satisfies 3x + 2y > 1, substitute each pair. For (2, 4): 3(2) + 2(4) = 6 + 8 = 14 > 1. Thus, (2, 4) is a solution. The other pairs do not satisfy the inequality.

Justin charges $11 to mow a small lawn and $26 to mow a large lawn. He would like to make at least $130.

Write an inequality that describes the situation.

Let x = # of small lawns mowed and

Let y = # of large lawns mowed

• 11x + 26y ≥ 130

• 11x + 26y > 130

• 11x + 26y ≤ 130

• 11x + 26y < 130

Answer explanation

Justin's earnings from mowing small and large lawns can be represented as 11x + 26y. To ensure he makes at least $130, we use the inequality 11x + 26y ≥ 130, making this the correct choice.

Select the correct graph for each inequality.

• A

• B

• C

• D

Answer explanation

Graph B correctly represents the inequality, showing the appropriate shading and boundary line. The other options do not accurately depict the solution set for the given inequality.

Tags

CCSS.HSA.REI.D.12

Which of the following inequalities matches the graph?

• y > x + 2

• y < -x + 2

• y < 2x + 2

• y < x + 2

Answer explanation

The graph represents a region below the line y = x + 2, indicating that y is less than x + 2. Therefore, the correct inequality is y < x + 2.

Tags

CCSS.HSA.REI.D.12

Which of the following inequalities matches the graph?

• 4y + 3x < 20

• 4y - 3x < 20

• 4y + 3x > 20

• 4y - 3x > 20

Answer explanation

The graph represents the region above the line defined by 4y - 3x = 20. Since the area above this line is shaded, the correct inequality is 4y - 3x > 20.

Tags

CCSS.HSA.REI.D.12