Solving Systems of 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

What is the solution?

• One Solution

• No solution

• Infinitely Many Solutions

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

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. It turns out that the doughnuts were more popular than the coffee. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. Which equations could be used to determine the cost of the coffee?

• 10c + 5d = 14.25
  5c + 10d = 16.50

• 10c + 5d = 16.50
  5c + 10d = 14.25

• c + d = 10
  5c + 10d = 16.50

• c + d = 5
  5c + 10d = 16.50

Solve the system of equations:

3x + y = –14

–2x – y = 9

• (-5,1)

• (5,-1)

• (1,4)

• (-1,4)

Solve the system of equations:
–x – 7y = 9
–x + 9y = –23 

• (3, -4)

• (3,4)

• (-2,5)

• (5,-2)

Solve the system of equations:
 3x + 7y = 23
-3x - 7y  = -17

• no solution

• (0,6)

• infinite soutions

• (6,0)

Solve the system:
3x + y = 16
-3x + 3y = 24

• (2, -10)

• (-18, -10)

• (-2,15)

• (2, 10)

Solve the system of equations:
−4x + 9y = 9
    x − 3y = −6 

• (-9,-5)

• (-5,9)

• (9,5)

• (-5,-9)

Solve the system of equations:
2x – y = 17
  x – y = 10  

• (7,-3)

• (-3,7)

• (-8,3)

• (2,4)