Systems of Equations Adding

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

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

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

Identify which method for solving systems is being described by this fact: Equations must have like terms "stacked" up vertically, usually written in standard form.

• Graphing

• Substitution

• Elimination (adding or multiplying)

Identify which method for solving systems is being described by this fact: If like terms have a matching coefficient but not opposite values, take the opposite of every term in one equation.

• Graphing

• Substitution

• Elimination (adding or multiplying)

Identify which method for solving systems is being described by this fact: If like terms do not have a matching coefficient, multiplying one or both of the equations by a certain factor to transform the equations into a set of like terms with a matching set of coefficients.

• Graphing

• Substitution

• Elimination (adding or multiplying)

Identify which method for solving systems is being described by this fact: The solution to a system of equations must make both of the equations true.

• Graphing

• Substitution

• Elimination (adding or multiplying)

• All 3 methods

Identify which method for solving systems is being described by this fact: When solving the system a true statement results like 6 = 6 or 0 = 0 and the answer is Infinite Solutions.

• Graphing

• Substitution

• Elimination (adding or multiplying)

• All 3 methods

When using any of the 3 methods to solve a system of linear equations the resulting solution is the same no matter which method is used.

• True; using any method will result in the correct solution.

• False; the solution varies because the solution depends on which method is used.