Solve Linear and Quadratic Systems

When you graph the exact same equation twice,

• you will have no solution. 

• you will have one solution.

• you will have infinite solutions. 

• you will graph a giraffe. 

Solve the following system. What is the solution?

• (1, -2)

• (-2, 1)

• (-4, 1)

• (2, 1)

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

• (−6, −4) 

• Infinite number of solutions  

• No solutions

• (6, 4) 

Solve the system of equations below:
9x - 4y = 1
-3x + 8y = -47

• (3, -7)

• (-3, 7)

• (-3, -7)

• (-7, -3)

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. Which equations could be used to determine the cost of the coffee?

• 10c + 5d = 14.25
  5c + 10d = 16.50

• 10c + 5d = 16.50
  5c + 10d = 14.25

• c + d = 10
  5c + 10d = 16.50

• c + d = 5
  5c + 10d = 16.50

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. Write & solve using a system of linear equations.

• 10 Adult tickets, 11 children tickets

• 12 Adult tickets, 9 children tickets

• 60 Adult tickets, 44 children tickets

• 9 Adult tickets, 12 children tickets

Which ordered pair is not a solution to the given system of inequalities? The solutions are ordered pairs that lie where the shaded areas meet.

• (0, 0)

• (10, 1)

• (-2, -3)

• (1, 2)

Which ordered pair is a solution to the given system of inequalities?

• (0, 6) 

• (-1, 4)

• (2, 1)

• (3, 4)

Identify the solutions to the system of quadratic inequalities. Select all that apply.

• {(0, 1)}

• {(1, 0)}

• {(-1, 0)}

• {(0, -1)}

Solve the system. On your own piece of paper, make sure to also do a graph analysis.

y = x² - x - 90

y = x + 30

• (10, 2) and (-10, 42)

• (12, 42) and (-10, 20)

• (42, 1) and (20, -1)

• (2, 12) and (4, 5)