System of Equations by Substitution

The first step in solving using the substitution method is __________.

• get x by itself

• get y by itself

• get either variable by itself

• add the equations together

Which variable should you isolate first in the system?

• The x in the first equation

• The y in the first equation

• The y in the second equation

• The x in the second equation

Solve with substitution

x = -3y - 8

x - 2y = -3

• (5, -1)

• (-5, 1)

• (-5,-1)

• (1,-5)

What is the best method do you use?

x = 6y − 11

−2x − 3y = −7

• Graphing, because they are both in slope-intercept form

• Substitution because a variable is isolated (solved for)

3x + 2y = 8

-x + y = -11

• (-5,6)

• (6,-11)

• (-6,-5)

• (6,-5)

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

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