Common Core HSA.REI.C.6 worksheet

Question 1

Solve: 3x + 3y = −12 5x − 3y = 4 Type the solution like (2, −1).

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Question 2

Adult tickets cost 12 and child tickets cost 5. A school sold 38 tickets and took 267 in total. How many adult tickets were sold?

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Question 3

Solve the system: y = −4x − 1 −3x − y = 1 Type the solution like (2, −1).

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Question 4

How many solutions does this system have? −3x − 5y = −9 6x + 10y = 18

• A. Exactly one
• B. None
• C. Infinitely many

Question 5

To solve y = −2x + 4 and −4x − 3y = 0 by substitution, which is the correct next line?

• A. −4x − 3·−2x + 4 = 0
• B. −4x + 3(−2x + 4) = 0
• C. −4x − 3(−2x + 4) = 0
• D. −2x + 4 − 3y = 0

Question 6

Fatima buys 3 apples and 2 pears for 35 cents. Another day, 1 apple and 4 pears cost 45 cents. How much does one pear cost, in cents?

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Question 7

Bike hire A charges $2 plus $3 per hour. Bike hire B charges $4 plus $2.50 per hour. After how many hours do they cost the same?

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Question 8

Solve the system: x = 3y + 16 x + 4y = −19 Type the solution like (2, −1).

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Question 9

Solve: x + y + z = 0, x − y + 2z = 10, 2x + y − z = −16. What is x?

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Question 10

Solve: 5x + 6y = −15 2x − 3y = 21 Type the solution like (2, −1).

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Question 11

Solve: x − 2y = −2 2x − 6y = −6 Type the solution like (2, −1).

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Question 12

Priya buys 3 notebooks and 2 pens for $4.60. A friend buys 2 notebooks and 5 pens for $7.10. How much is one pen? Give the amount as a number.

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Question 13

How many solutions does this system have? y = −2x y = −4x + 5

• A. Exactly one
• B. None
• C. Infinitely many

Question 14

Solve: 4x − 5y = 6 4x − 2y = 12 Type the solution like (2, −1).

Answer 

Question 15

The sum of two numbers is 89 and their difference is 9. What is the larger number?

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Question 16

Which first move eliminates y straight away? 5x + 6y = 9 2x − 6y = −4

• A. Add the equations
• B. Subtract the equations
• C. Multiply one equation first