Solving Systems Using Substitution and Elimination

Three chairs and two tables cost $700 and five chairs and six tables cost $1100. Find the cost of each chair.

• 7 and 23

• 100

• 45 and 15

• 45

Elimination

3x − 2y = 4

5x + 3y = -25

• (-2, -5)

• (4,6)

• (-5,-4)

• (3,7)

Elimination

2x − 4y = -26

3x − y = -24

• (6,9)

• (-7,3)

• (5,-8)

• (-2,-4)

Substitution

y = − 3x

y = 6x − 9

• (1, − 3)

• (3, 7)

• (4, − 2)

• ( − 4, 8)

Substitution

2x + y = − 7

5x + 3y = − 21

• (4, − 3)

• ( − 1, 0)

• (0, − 7)

• ( − 4, 8)

Substitution
y = − 6 
3x − 6y = 30

• (1, 3)

•  ( − 2, − 6)

• (0, − 7)

• ( − 4, 8)

Elimination

− 6x + 9y = 3

6x − 9y = − 9

• ( − 3, − 5)

• (0,-4)

• Infinite number of solutions

• No solution

Ms. Kitts works at a music store. Last week she sold 6 more than 3 times the number of CDs that she sold this week. Ms. Kitts sold a total of 110 CDs over the 2 weeks. Which system of equations can be used to find l, the number of CDs she sold last week, and t, the number of CDs she sold this week?

• l + t = 108

  l = 3t + 6

• l = 3w 2

  (l + w) = 85

• 2s + 3b = 156

  s = b + 8

• m + n = 54

  m = 3n + 8

Maricella has a bag containing 35 nickels and quarters. The total value of these coins is less than $2.50. What is the maximum number of quarters that meets these conditions?

• 3

• 7

• 4

• 1

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. How many toppings need to be added to a large cheese pizza from Palanzio’s Pizzeria and Guido’s Pizza in order for the pizzas to cost the same, not including tax?

• 5

• 9

• 2

• 0