Problem Solving Systems of Linear Equations

Last season two running backs on the Steelers football team rushed a combined 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

• y = 1550 + x
  y = x + 4

Josh is thinking of two numbers.  Their sum is -10 and their difference is -2.  Which system of equations represents the situation?

• x - y = -10
  x + y = -2

• x = -2 
  y = 5

• x + y = -2
  x - y = -10

• x + y = -10
  x - y = -2

At a college bookstore, Carla purchased a math textbook and a novel 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

• t + n = 8
  t = 3n + 54

The difference of a and b is 3. The sum of the variables is 13. Find the numbers.

• a = 7
  b = 10

• a = 8
  b = 5

• a = 10
  b = 13

Solve by elimination:
4x+9y=28
-4x-y=-28

• (-7,0)

• (6,0)

• (-6,0)

• (7,0)

Solve by elimination:

3x+7y=23

-3x-7y=-17

• No solution

• (0, 3)

• (-3,3)

• (3,3)

Solve by elimination:

7x+y=-9

-3x-y=5

• No solution

• (-1,8)

• (-2,-3)

• (-1,-2)

Solve by elimination:
4x+4y=4

3x+4y=10

• (7,-6)

• (-6,7)

• (6,7)

• (7,6)

Solve by elimination:
-x+2y=17

2x+2y=-10

• ARN

• (-9,4)

• (-9,-4)

• (9,-4)

Solve by elimination

4x-6y= -6

-2x-12y= -12

• (0,1)

• (1,0)

• (1,1)

• (0, 2)