Systems of Linear Equations Mixed

Sam has a total of 17 bikes, unicycles, and skateboards. A bike has 2 wheels, a skateboard has 4 wheels, a unicycle has one wheel and she has a total of 42 wheels. There are just as many bikes as unicycles and skateboards together. Which system models this scenario?

• B + U + S = 42

  2B + U + 4S = 17

  B = U + S

• B + U + S = 17

  2B + U + 4S = 42

  B = U + S

• B + U + S = 17

  2B + U + 4S = 42

  B = U*S

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

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

Solve the system of equations: 

• ( 4, 0, -2)

• ( -4, -2, 0)

• None of these

• ( -4, 0, -2)

Solve the following system by graphing. What is the solution? (Graph on your scratch paper!)

• (3, -1)

• (-1, -3)

• (-1, -1)

• (-1, 3)

Solve using SUBSTITUTION: (Show your work on scratch paper!)

y = -1x - 5

4x - 8y = 4

• (-3, -2)

• (5, -7)

• (3, 9)

• (-5, 4)

Solve using ELIMINATION. (Show your work on scratch paper!)

3x + 2y = 16

7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

Solve using SUBSTITUTION. (Show your work on scratch paper!)

x-2y=1

x+4y=7

• (3, 1)

• (-1, -1)

• (1, 3)

• (4, 1)

When you graph the exact same equation twice,

• you will have no solution. 

• you will have one solution.

• you will have infinite solutions. 

• you will graph a giraffe. 

Solve by graphing. (Graph on your scratch paper!) y = 2x + 1 y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)