Quiz about Linear Inequalities

Question 1

Which point would be a solution to the system of linear inequalities shown below?

$$y<4x-2$$

$$y\le-\frac{5}{4}x-3$$

Accepted Answer

(0, -6)

Answer

(12, -8)

Answer

(4, -4)

Answer

(-4, -10)

Question 2

Which point would be a solution to the system of linear inequalities shown below?

$$y\ge2x+2$$

$$y>\frac{1}{2}x-1$$

Accepted Answer

(-6, -3)

Answer

(8, -8)

Answer

(6, 3)

Answer

(10, 7)

Question 3

Which points would not be a solution to the system of linear inequalities shown below?

$$y>-4x+6$$

$$y>\frac{1}{3}x-7$$

Accepted Answer

(9, -7)

Accepted Answer

(-12, -2)

Accepted Answer

(-12, -7)

Answer

(12, 1)

Question 4

Solve the following system of inequalities graphically. State the coordinates that are in the solution set.

$$y>-x-1$$

$$3x+3y\ge-9$$

Accepted Answer

(2,-2)

Accepted Answer

(-2,5)

Answer

(1,-2)

Answer

(-3,-5)

Question 5

Kaylee is working two summer jobs, making $7 per hour babysitting and making $15 per hour clearing tables. In a given week, she can work no more than 30 total hours and must earn at least $210. If x represents the number of hours babysitting and y represents the number of hours clearing tables, write a system of inequalities. Give each inequality in slope-intercept form.

Accepted Answer

$$y\le-x+30$$

Accepted Answer

$$y\ge-\frac{7}{15}x+14$$

Answer

$$y\ge-x+30$$

Answer

$$y\ge-\frac{1}{2}x+14$$

Question 6

The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $5.50 and each adult ticket sells for $8.50. The auditorium can hold at most 130 people. The drama club must make a minimum of $700 from ticket sales to cover the show's costs. If x represents the number of student tickets sold and y represents the number of adult tickets sold, write a system of inequalities. Give each inequality in slope-intercept form and round your answer to the nearest penny.

Accepted Answer

$$y\le-x+130$$

$$y\ge-0.73x+93.33$$

Answer

$$y\ge-0.5x+50$$

$$y\le-x+130$$

Answer

$$y\le-x+150$$

$$y\le-0.73x+93$$

Answer

$$y<-x+130$$

$$y\le-0.73x+93.33$$

Question 7

Choose the inequality that matches the graph shown.

Accepted Answer

$$2x+y\le-8$$

Answer

$$2x-y\le8$$

Answer

$$-4x-8y>16$$

Answer

$$4x+8y<64$$

Question 8

Select the correct graph for each inequality.

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Linear Inequalities

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