Solving Equations and Graphing Inequalities

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

This system has _____ solutions

• 0

• 1

• 2

• Infinitely many

Which ordered pair is one of the solutions to the system of inequalities?

• (2, 0)

• (1, 1)

• (4, -3)

• (-2, 2)

The owner of Mark's Meat Market orders beef and chicken. He wants to but at least 50 pounds of meat but cannot spend more than $300. Beef is $3 a pound and chicken is $2 a pound.
Which system of inequalities models this situation?

Which ordered pair(s) is a solution to the given system?

• (5, -5)

• (0,0)

• (-5, -2)

• (3,-3)

This system has _____ solutions

• 0

• 1

• 2

• Infinitely many

You can solve systems using these methods:

• graphing, substitution, and elimination

• rearranging, thinking, and guessing

• only by graphing

If the solution is infinitely many the lines will ________?

• intersect at exactly one point

• be parallel

• overlap each other

• never exist

Steffen graphed two lines in order to find the solution to a given system of equations.
What is the solution?

• (-3,-8)

• (-8,-3)

• (3,-8)

• (8,3)

Give the solution to the system

• (3,1)

• (1,3)

• (-1,3)

• No solution