Applying Systems of Linear Equations

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

• 1.5x+0.5y=78.5
  x+y=87
• 1.5x+0.5y=78.5
  1.5x+0.5y=87
• x+y=78.5
  1.5x+0.5y=87
• x+y=78.5
  x+y=87

Tags

CCSS.HSA.CED.A.3

Which of the following are ways to solve systems of equations? 

• Graphing
• Substitution
• Elimination
• All of the above

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Does the following system have One Solution, No Solution, or Infinite Solutions.  
y = 4x + 8
y = -5x + 3

• One solution
• No solution
• Infinite solution

Tags

CCSS.8.EE.C.8B

Solve for x and y
y = 2x + 1
y = 4x - 1

• (1,3)
• (-1,-3)
• (-1,3)
• (3,1)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

What is the solution to the system?
8x + 4y = 12
y = -2x + 3

• (0,3)
• (3,0)
• No solution(parallel lines)
• Infinitely many solutions

Tags

CCSS.8.EE.C.8B

Determine if (4, 1) is a solution for the system of equations.
y = -x + 5
y = 2x - 7

• yes
• no

How many solutions will this system have? 

• No solution
• One Solution
• I Don't Know
• Infinitely Many Solutions

Tags

CCSS.8.EE.C.8A

Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)
• (-2,-5)
• (2,-5)
• (2,5)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve the system using any method. 
−4x − 4y = 0
4x + 4y = 0 

• (−6, −4) 
• Infinite number of solutions  
• No solutions
• (6, 4) 

Tags

CCSS.8.EE.C.8B

How can you tell if a point is a solution to a system?

• It makes the first equation true.
• The (x,y) coordinates satisfy both equations
• It makes logical sense
• It makes neither equation negative