Setting Up Substitution Problems

Ben ordered 20 total items consisting of pizza and sodas.  A pizza is $10, a soda is $2, and he spent a total of $72.  Which system models this scenario?

• 10P + 2S = 20
  P + S = 72

• P + S = 20
  2P + 10S = 72

• P + S = 20
  10P + 2S = 72

• y = 10x + 2

  y = 72x + 20

Tags

CCSS.HSA.CED.A.3

Rachel buys 3 tricycles and 4 bicycles for a total of $72. Joe bought 5 tricycles and 2 bicycles for $50.  Which system models this scenario?

• 3B + 5T = 72
  2T + 4B = 50

• 3T + 4B = 72
  5T + 2B = 50

• 3T + 4B = 50
  5T + 2B = 72

• y = 3x + 4

  y = 5x + 2

Tags

CCSS.8.EE.C.8C

Mr. Riley bought 8 tickets to a chili supper and spent a total of $30. He bought a combination of adult tickets for $5 each and child tickets $3 each. Which system of equations below will determine the number of child tickets, c, and the number of adult tickets, a, he bought?

• y = 8x + 30

  y = 5x + 3

• a + c = 8

  3a + 5c = 30

• 5a + 3c = 8

  a + c = 30

• 5a + 3c = 30

  a + c = 8

Tags

CCSS.HSA.CED.A.3

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 = .90x + 6.80
  y = .65x + 7.30

• y + .90x = 6.80
  y + .65x = 7.30

Tags

CCSS.8.EE.C.8C

Solve for x and y (Use Substitution)

y = 2x + 1

y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

• (1,1)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve the system of linear equations by substitution.

-5x + 3y = 51

y = 10x - 8​

​ ​ ​ (a)   ​ (b)  

• y = -22

• x = -3

• x = 59/25

• y = 15.6

• x = 3

• y = 22

• x = -8

• y = 4

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve using Substitution Method

y = -6

-3x - 6y = 24

• (6, 6)

• (6, -6)

• (4, -6)

• (-6, 4)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve for x and y using the substitution method.

5x + 3y = 7

y = 4

• (4,1)

• (4,-1)

• (1,4)

• (-1,4)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

If 2x+3y = 12 and 3x-2y=5 then

• x = 2, y = 3

• x = 2, y = -3

• x = 3, y = 2

• x = 3, y = -2

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

solve by substitution: y=3x+14

• (2, 8)

• (-2, -6)

• (-2, 8)

• (-2, -4)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6