Practice Systems of Equations

Solve by elimination: 7x - 9y = 29 7x + 2y = - 15

• (-4,-1)

• (-1.-4)

• (-1,4)

• (-1,6)

x = y - 2
4x + y = 2

• (2,0)

• (0,2)

• (0, -2)

• (-2,0)

At a college bookstore, Carla purchased a math textbook that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

• t + n = 54

  t = 3n + 8

• t + n = 54

  n = 3t + 8

• t + n = 54

  t = 3n - 8

• 8 + 3t = n

  54 = 8t + 3n

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out (all) the coins and it came to $6.60. Which system of equations could be used to find the exact number of dimes and nickels? (Hint: How much are the coins worth?)

• d + n = 6.60

  .10d + .05n = 80

• d + n = 80

  d + n = 6.60

• d + n = 80

  .10d + .05n = 6.60

Last season two running backs on the Steelers football team rushed a combined (both running backs) total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed. Which system of equations could be used?

• x + y = 1550

  y = 4x

• x + y = 1550

  y = x + 4

• y - x = 1550

  y = 4x

A system of equations is a set of _________ or more equations.

• 0

• 1

• 2

A system of equations always has the same ___________ and ___________.

• equations and variables

• equations and solutions

• letters and numbers

• variables and solutions

A __________ is a value that makes all equations in a system true.

• solution

• number

• variable

• letter

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

• t = 9.65 + s

  t = 8.40 + s

• t = 9.65s + 43

  t = 8.40s + 58

• t =9.65s

  t = 8.40s

• 9.65 = s + 43

  8.40 = s + 58

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables?

• t: # of tacos

  m: # of glasses of milk

• t: Cost of each taco

  m: Cost of each glass of milk

• t: total cost

  m: # of food items