Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Where x is the number of hair cuts and y represents the hair dyes. After solving the system below, Alexandra gets a solution of (45,90) 3x + 2y = 315 2x + 4y = 450 What does the solution (45,90) mean?

Haircuts take Alexandra 45 minutes & hair dyes take 90 minutes.

Hair dyes take Alexandra 45 minutes & haircuts take 90 minutes.

Haircuts cost $45 & hair dyes cost $90.

Hair dyes cost $45 & haircuts cost $90.

Caroline is considers 2 video game rental plans. Plan A can be modeled with the equation $$C=2n$$ , and Plan B is modeled with the equation $$C=n+6$$ , where C represents the cost in dollars & n represents the number of games rented each month. The solution to this situation is $$n=6$$ & $$C=12$$ . What do these numbers mean?

If Caroline orders 6 games each month, both plans will cost $12.

Caroline can order 12 games from Plan A & 6 games from Plan B.

If Caroline orders 12 games each month, both plans will cost $6.

Caroline can order 6 games from Plan A & 12 games from Plan B.

Naomi is working two jobs, making $10 per hour washing cars and $12 per hour tutoring. Last week, Naomi earned a total of $108 and worked 2 more hours washing cars than hours tutoring. The system of linear equations that represents this situation is given below. Let x = the number of hours Naomi washed cars Let y = the number of hours Naomi tutored 10x + 12y = 108 x = y + 2 Solve the system, and interpret the solution in the context of the problem. Hint: the Substitution Method may be easier here!

(6, 4) --> Naomi spent 6 hours washing cars and 4 hours tutoring

(4, 6) --> Naomi spent 4 hours washing cars and 6 hours tutoring

(6, 4) --> Naomi spent 6 hours tutoring and 4 hours washing cars

(4, 6) --> Naomi spent 4 hours tutoring and 6 hours washing cars

Megs went to the grocery store to purchase cans of soup and frozen dinners. Each can of soup has 350 milligrams (mg) of sodium (salt), and each frozen dinner has 650 mg of sodium. Megs purchased a total of 11 cans of soup and frozen dinners, which collectively contain 4750 mg of sodium. Solve the system given below to determine the number of cans of soup and the number of frozen dinners Megs purchased. Hint: both the Substitution and Elimination Methods may be used here! 350c + 650f = 4750 c + f = 11

Megs purchased 8 cans of soup and 3 frozen dinners

Megs purchased 3 cans of soup and 8 frozen dinners

Megs purchased 9 cans of soup and 12 frozen dinners

Megs purchased 12 cans of soup and 9 frozen dinners

Isaac is going to a carnival that has games and rides. Each game costs $1.50 and each ride costs $5. Isaac spent $44.50 altogether, and the number of rides he went on is 5 more than the number of games he played. This situation is represented by the system below. r = g + 5 1.50g + 5r = 44.50 Determine the number of games Isaac played and the number of rides Isaac went on. Hint: the Substitution Method may be easier here!

Isaac played 3 games and went on 8 rides.

Isaac played 8 games and went on 3 rides.

Isaac played 26 games and went on 31 rides.

Isaac played 31 games and went on 26 rides.

A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 6 cubic feet and the volume of each large box is 15 cubic feet. There were 2 more small boxes shipped than large boxes, and the total volume of all boxes was 243 cubic feet. Let x = the number of small boxes shipped Let y = the number of large boxes shipped x = y + 2 6x + 15y = 243 Find the solution to this system of equations, and interpret the solution in the context of the problem.

(13, 11) --> 13 small boxes and 11 large boxes will be sent

(11, 13) --> 13 small boxes and 11 large boxes will be sent

(13, 11) --> 11 small boxes and 13 large boxes will be sent

(11, 13) --> 11 small boxes and 13 large boxes will be sent

Interpret Systems of Equations

Authored by Anthony Clark

Mathematics

8th Grade

CCSS covered

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20 questions

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

Decide which ordered pair would be the solution to BOTH equations

Tags

CCSS.HSA.REI.C.9

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Determine which ordered pair is a solution to BOTH of the equations

(0,4)

(3,0)

(-4,5)

(5,-4)

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which system of equations can be used to determine s, the number of senior citizen tickets sold and c, the number of children tickets sold?

s + 3c = 38

2s + 3c = 52

3s + 1c = 38

3s + 2c = 52

s + c = 38

s + c = 52

3s + 3c = 38

1s + 2c = 52

Tags

CCSS.HSA.CED.A.3

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount?

y = 9.65 + x
y = 8.40 + x

y = 9.65x + 43
y = 8.40x + 58

y =9.65x
y = 8.40x

y = 9.65x - 43
y = 8.40x - 58

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Solve the system.

(3, -2, 4)

(2, -3, 1)

(-3, 2, -1)

Infinitely many solutions

MULTIPLE CHOICE QUESTION

1 min • 1 pt

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

4y = 3x + 64

8y = x + 68

4y = 3x + 64

8y = x + 60

3x + 4y = 64

x + 8y = 68

3x + 4y = 64

x + 8y = 60

Tags

CCSS.8.EE.C.8C

MULTIPLE CHOICE QUESTION

1 min • 1 pt

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $68 for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

4y = 3x + 64

8y = x + 68

4y = 3x + 64

8y = x + 60

3x + 4y = 64

x + 8y = 68

3x + 4y = 64

x + 8y = 60

Tags

CCSS.HSA.CED.A.3

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Interpret Systems of Equations

Decide which ordered pair would be the solution to BOTH equations

Determine which ordered pair is a solution to BOTH of the equations

Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount?

Solve the system.

Two linear equations with the same set of variables

Solve the system.

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