System of Equations and 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

A gym charges a one-time registration fee as well as a monthly fee. The cost of joining the gym for 4 months is $370, and the cost of joining for 6 months is $530. Write a system of equations to find the registration fee and monthly fee. m= months; r = registration fee.

• r - 4m = 370
  r - 6m = 530

• r + 4m = 370
  r + 6m = 530

• m + 4r = 370
  m + 6r = 530

• m - 4r = 370
  m - 6r = 530

Christian had brochures printed for a new business venture. Christian originally ordered 4 boxes of black-and-white brochures and 3 boxes of color brochures, which cost a total of $134. After those ran out, Christian spent $120 on 3 boxes of black-and-white brochures and 3 boxes of color brochures. Which system represents this situation?

• x+y=134
  x+y=120

• 3x+3y=134
  4x+3y=120

• 4x+3y=134
  3x+3y=120

• 7xy=134
  6xy=120

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.

• x + y = 33
  y = 2x - 3

• x + y = 33
  x = 2y - 3

• x + y = 33
  x = 3 - 2y

• x + y = 3
  x = 33 - 2y

Solve by using substitution method.

• (2, 7)

• (0, 1)

• (2/5, 9/5)

• (2, 5)

Solve by using elimination method.

• (3, 1)

• ( 5, -5)

• (2, 5)

• (15, 1)

For equations below, which method is easier to use? Why?

• Graphing, because both are already in y = mx + b form.

• Substitution, because one equation is already solved for y. 

• Elimination, because both are already in ax + by = c form. 

• None. 

For equations below, which method is easier to use? Why?

• Graphing, because both are already in y = mx + b form.

• Substitution, because one equation is already solved for y. 

• Elimination, because both are already in ax + by = c form. 

• None. 

A system has ____________ when two lines intersect at one point. 

• One solution

• No solution

• Infinitely Many Solution

A system has ____________ when two equations are exactly the same and overlap each other.

• One solution

• No solution

• Infinitely Many Solution