Search Header Logo

Checking solutions of two-variable inequalities (Math Masters)

Authored by Ben Nguyen

Mathematics

8th Grade

Checking solutions of two-variable inequalities (Math Masters)
AI

AI Actions

Add similar questions

Adjust reading levels

Convert to real-world scenario

Translate activity

More...

    Content View

    Student View

15 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

What is the general form of a two-variable inequality?

Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C

Ax + By + C > 0

Ax + By ≠ C

Ax + By = C

Answer explanation

The general form of a two-variable inequality includes expressions like Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C. These represent different relationships between the variables and a constant.

2.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

Which of the following points is a solution to the inequality y>3x+4?

(0, 5)

(3, 4)

(1, 2)

(2, 3)

Answer explanation

To solve the inequality y > 3x + 4, substitute the points. For (0, 5): 5 > 3(0) + 4, which is true. For (3, 4): 4 > 3(3) + 4 is false. For (1, 2) and (2, 3), both are false. Thus, (0, 5) is the only solution.

3.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

How do you determine if a point is a solution to a two-variable inequality?

Graph the inequality and find the intersection point.

Substitute the point into the inequality and check if the statement is true.

Choose any random point and assume it is a solution.

Check if the point lies on the boundary line only.

Answer explanation

To determine if a point is a solution to a two-variable inequality, substitute the point into the inequality. If the resulting statement is true, then the point is a solution. This method directly verifies the point's validity.

4.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

What does the boundary line represent in a two-variable inequality?

The boundary line shows the area where solutions are not valid.

The boundary line represents the points where the corresponding equation is equal.

The boundary line indicates the maximum value of the inequality.

The boundary line represents the average of the two variables.

Answer explanation

The boundary line in a two-variable inequality represents the points where the corresponding equation is equal. It separates the solution region from the non-solution region, indicating where the inequality holds true.

5.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

For the inequality y≤x-4 which of the following points is NOT a solution?

(2, -3)

(5, 1)

(3, 0)

(0, -5)

Answer explanation

To check which point is NOT a solution for y≤x-4, substitute each point. For (3, 0): 0 ≤ 3-4 is false. Thus, (3, 0) is NOT a solution, while the others satisfy the inequality.

6.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

If the inequality is y<1x/2+1, what is the correct way to graph it?

Graph the line y = (1/2)x + 1 as a dashed line and shade below it.

Graph the line y = (1/2)x + 1 as a dashed line and shade above it.

Graph the line y = (1/2)x + 1 and do not shade any area.

Graph the line y = (1/2)x + 1 as a solid line and shade above it.

Answer explanation

To graph the inequality y < (1/2)x + 1, first graph the line y = (1/2)x + 1 as a dashed line, indicating that points on the line are not included. Then, shade below the line to represent all y-values less than the line.

7.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

Which of the following statements about the solution set of a two-variable inequality is true?

The solution set is a single point in the coordinate plane.

The solution set can only be represented as a line segment.

The solution set is a region in the coordinate plane.

The solution set is always empty for two-variable inequalities.

Answer explanation

The correct choice is that the solution set is a region in the coordinate plane. Two-variable inequalities typically represent areas, such as half-planes, rather than just points or line segments.

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Google

Continue with Google

Email

Continue with Email

Classlink

Continue with Classlink

Clever

Continue with Clever

or continue with

Microsoft

Microsoft

Apple

Apple

Others

Others

Already have an account?