Solving Equations by Substitution

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping.The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings when both companies cost the same amount?

• y = 6.80 + .65x

  y = 7.30 + .90x

• x + y = 6.80

  x + y = 7.30

• y = 6.80 + .90x

  y = 7.30 + .65x

• y + .90x = 6.80

  y + .65x = 7.30

Dustin and his workout partner are lifting weights together, doing many sets of each exercise. On a certain exercise, Dustin is using a 35-kilogram bar, increasing the amount of weight he lifts by 3 kilograms on each set. His partner, meanwhile, started out using a 40-kilogram bar and is upping the weight by adding 2 kilograms on every set. Eventually, Dustin and his workout partner will be lifting the same amount, and will take turns using the same barbell. How much weight will they be lifting then? Write a system of equations in order to find the solution.

• 75 kilograms

• 5 kilograms

• 50 kilograms

• 80 kilograms

Solve for x and y
y = 2x + 1
y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

y = -6x + 5
-2x + y = 5

• (-3, -6)

• (-6, 3)

• (0, 5)

• (-3, 5)

Solve the system by substitution. 
-2x - 2y = 16
y = -8

• (0, -8)

• (-8, 0)

• (-16, -8)

• (-16, -8)

Solve the system by substitution. 
y = 2x − 11 
2x − 8y = 4 

•  (6, 1)

• (6, −4)

• (6, −1)

• Infinite number of solutions  

Solve the system by substitution. 
3x − 2y = 7 
y = 2x − 7 

• No solution 

•  (7, 7)  

•  (−7, −7)  

•  (−7, −3)  

What is the solution to the system of equations? (use Substitution)
y - 3x = -8
y = 4 - x

• (3,1)

• (-3,1)

• (1,3)

• (3,-1)

Solve:
y=8x+1
y=6x+3

• (1, 9)

• (4, 14)

• (0, 1)

• (2, 4)

Solve the system by substitution. 
-5x - 4y = -9
y = 6

• (3, 6)

• (6, -3)

• (-3, 6)

• (6.8, 3)