Topic 4 Review: Systems of Linear Equations and Inequalities

Topic 4 Review: Systems of Linear Equations and Inequalities

by P. Spivey

Multiple Choice

A(n) _____ is made up of two or more inequalities.

• linear inequality in two variables

• solution of an inequality in two variables

• solution of a system of linear inequalities

• system of linear inequalities

Multiple Choice

A(n) _____ is an inequality that is in the same form as a linear equation in two variables, but with an inequality symbol instead of an equal sign.

• linear inequality in two variables

• solution of an inequality in two variables

• solution of a system of linear inequalities

• system of linear inequalities

Multiple Choice

A(n) _____ is an ordered pair that makes all of the inequalities in the system true.

• linear inequality in two variables

• solution of an inequality in two variables

• solution of a system of linear inequalities

• system of linear inequalities

Multiple Choice

The _____ is the set of all ordered pairs that satisfy the inequality.

• linear inequality in two variables

• solution of an inequality in two variables

• solution of a system of linear inequalities

• system of linear inequalities

Multiple Choice

Which graph shows the solution to the system?

$$y=5x+4$$  

$$y=−3x−8$$  

Multiple Choice

Describe the solution set of the system of equations made by the equation $$y=1.5x+4.5$$  and the graphed line.

• No Solution

• Infinitely Many Solutions

• One Solution

  ( $$\frac{17}{6}$$  , $$\frac{1}{4}$$ )

• One Solution

  ( $$-\frac{17}{6}$$  , $$\frac{1}{4}$$ )

Multiple Choice

Kiyo is considering two catering companies for a party. A+ Food charges $35 per person and $75 to setup. Super Cater charges $38 per person with no setup fee. Write a system of equations to represent the charges for catering by each company.

• A+ Food $$y=35x+75$$  

  Super Cater $$y=38x$$  

• A+ Food $$y=75x\ +\ 35$$  

  Super Cater $$y=0x+38$$  

• A+ Food $$y=35x+75x$$  

  Super Cater $$y=38x$$  

• A+ Food $$y=35+75$$  

  Super Cater $$y=38$$  

Multiple Choice

Kiyo is considering two catering companies for a party. A+ Food charges $35 per person and $75 to setup. Super Cater charges $38 per person with no setup fee. How many people would Kiyo have to invite to pay the same price for both companies? What is the price she would pay?

• Kiyo would have to invite 20 guests to the party and would pay $850

• Kiyo would have to invite 25 guests to the party and would pay $950

• Kiyo would have to invite 850 guests to the party and would pay $20

• Kiyo would have to invite 950 guests to the party and would pay $25

Multiple Choice

Kiyo is considering two catering companies for a party. A+ Food charges $35 per person and $75 to setup. Super Cater charges $38 per person with no setup fee. Which company should Kiyo use if she expects 28 guests?

• Kiyo should use A+ Food if

  she expects 28 guests.

• Kiyo should use Super Cater if

  she expects 28 guests.

Multiple Choice

Solve the system of equations using substitution.

$$3y=3x−9$$  

$$y−2=x$$  

• Infinitely Many Solutions

• ( $$-\frac{15}{2}$$ , $$-\frac{11}{2}$$ )

• No Solution

• (0, -9)

Multiple Choice

A room has a perimeter of 40 feet. The length is 4 less than 2 times the width. Write a system of equations to represent the relationship between the length and width of the room.

• $$2\left(l+w\right)=40$$   $$l=2w-4$$  

• $$2\left(l+w\right)=40$$   $$l=2\left(w-4\right)$$  

• $$2\left(l+w\right)=40$$   $$l=4-2w$$  

• $$2l+2w=40$$   $$l=4-2w$$  

Multiple Choice

A room has a perimeter of 40 feet. The length is 4 less than 2 times the width. What are the dimensions of the room?

• 10 feet long and 6 feet wide

• 14 feet long and 10 feet wide

• 8 feet long and 12 feet wide

• 12 feet long and 8 feet wide

Multiple Choice

Solve the system of equations using elimination.

$$4x-3y=14$$  

$$12x\ -9y=42$$  

• Infinitely Many Solutions

• (16, -12)

• No Solution

• ( $$\frac{7}{2}$$  , $$-\frac{14}{3}$$  )

Multiple Choice

Carmen and Alicia go to the office supply store to purchase packs of pens and paper. Carmen bought 5 packs of paper and 3 packs of pens for $36.60. Alicia bought 6 packs of paper and 6 packs of pens for $53.40. Write a system of equations to represent the pens and paper purchased.

• $$5x+3y=53.40$$ $$6x+6y=53.40$$

• $$5x+3y=36.60$$ $$6x+6y=36.60$$

• $$5x-3y=36.60$$ $$6x-6y=53.40$$

• $$5x+3y=36.60$$ $$6x+6y=53.40$$

Multiple Choice

Carmen and Alicia go to the office supply store to purchase packs of pens and paper. Carmen bought 5 packs of paper and 3 packs of pens for $36.60. Alicia bought 6 packs of paper and 6 packs of pens for $53.40. What is the price of one pack of paper and one pack of pens?

• One pack of pens costs $3.95 and one pack of paper costs $4.95.

• One pack of pens costs $4.95 and one pack of paper costs $3.95.

• One pack of pens costs $3.15 and one pack of paper costs $4.15.

• One pack of pens costs $4.15 and one pack of paper costs $3.15.

Multiple Select

Use the graph to select the ordered pair(s) that are solutions of the inequality $$y\ge2x−3$$  .

• (2,5)

• (3,-1)

• (-2,4)

• (3,3)

Multiple Choice

Select the linear inequality represented by the graph.

• $$y>\frac{3}{2}x+4$$  

• $$y<\frac{3}{2}x+4$$  

• $$y\le\frac{3}{2}x+4$$  

• $$y\ge\frac{3}{2}x+4$$  

Multiple Choice

Renaldo has a budget of $500 to buy gift boxes for a party. Large boxes cost $65 and small boxes cost $35. Write an inequality that represents the number of each type of gift box that Renaldo can buy.

• $$65x+35y<500$$  

• $$65x+35y=500$$  

• $$65x+35y\le500$$  

• $$65x+35y\ge500$$  

Multiple Choice

Renaldo has a budget of $500 to buy gift boxes for a party. Large boxes cost $65 and small boxes cost $35. If Renaldo buys 6 small gift boxes, how many large gift boxes can he afford to buy?

• Renaldo can afford 3 large gift boxes.

• Renaldo can afford 7 large gift boxes.

• Renaldo can afford 1 large gift box.

• Renaldo can afford 4 large gift boxes.

Multiple Choice

Olivia makes and sells bracelets and necklaces. She can make up to 60 pieces per week, but she can only make up to 40 bracelets and 40 necklaces. Write a system of inequalities that shows the combination of bracelets and necklaces that she can make if she wants to sell at least 30 items per week.

• $$x+y\le60$$   $$x\le40$$   $$y\le40$$   $$x+y\ge30$$  

• $$x+y<60$$   $$x\le40$$   $$y\le40$$   $$x+y>30$$  

• $$x+y\le60$$   $$x<40$$   $$y<40$$   $$x+y\ge30$$  

• $$x+y\ge60$$   $$x\le40$$   $$y\le40$$   $$x+y\le30$$  

Multiple Choice

Olivia makes and sells bracelets and necklaces. She can make up to 60 pieces per week, but she can only make up to 40 bracelets and 40 necklaces. She wants to sell at least 30 items per week. If necklaces sell for $80 each and bracelets sell for $5 each, what is the most money she can make in a week?

• The maximum is $3,300 for

  40 necklaces and 20 bracelets.

• The maximum is $1,800 for

  20 necklaces and 40 bracelets.

• The maximum is $1,300 for

  15 necklaces and 20 bracelets.