Substitution and Equations: Write Equations with Models

Solve:

x = -3y - 17

2x + 3y = -7

• (1, -20)

• (10, 0)

• (-5, -2)

• (10 , -9)

3x + 2y = 8

-x + y = -11

• (-5,6)

• (6,-11)

• (-6,-5)

• (6,-5)

What is the solution to the system of equations?

y = 3x - 8

y = 4 - x

• (3,1)

• (1,3)

• (3,-1)

• (3,-1)

Solve the system of equations.

y = -5x

x + 3y = 28

• (-6, 30)

• (-2, 10)

• (-2, 39)

• No solution

• Infinite solutions

Solve:

y = 8x+1

y = 6x+3

• (1, 9)

• (4, 14)

• (0, 1)

• (1, 4)

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

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

• y = 9.65 + x

  y = 8.40 + x

• y = 9.65x + 43

  y = 8.40x + 58

• y = 9.65x

  y = 8.40x

• y = 9.65x - 43

  y = 8.40x - 58

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

For his parents' anniversary party, Felix is considering using one of two venues. A hotel in Arcadia will cost $400 for a reservation, plus $30 per person. A restaurant in the same city will cost $10 per person, in addition to $800 for the reservation. In order to make the best decision, Felix figures out how many guests it would take to have the venues cost the same amount. How many guests would that be?

Write a system of equations in order to determine the solution.

• 20 guests

• 1000 guests

• 1200 guests

• 200 guests

y = -6x + 5

-2x + y = 5

• (-3, -6)

• (0, 3)

• (0, 5)

• (-3, 5)