Solving Systems by Substitution of Equations

For his parents' anniversary party, Felix is considering using one of two venues. A hotel in Arcadia will cost $400 for a reservation, plus $30 per person. A restaurant in the same city will cost $10 per person, in addition to $800 for the reservation. In order to make the best decision, Felix figures out how many guests it would take to have the venues cost the same amount. How many guests would that be? Write a system of equations in order to determine the solution.

• 20 guests

• 1000 guests

• 1200 guests

• 200 guests

y = -6x + 5

-2x + y = 5

• (-3, -6)

• (0, 3)

• (0, 5)

• (-3, 5)

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

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

y = -2x + 5
y = 2x - 11

• No Solution

• (0, 0)

• (3, -1)

• (4, -3)

Solve:
y = 2x -11
-3y = -6x -15

• (-1.5,-4)

• (1.5,4)

• No solution (parallel lines)

• Infinitely many solutions

y = -6x + 5
-2x + y = 5

• (-3, -6)

• (-6, 3)

• (0, 5)

• (-3, 5)

y = -3x + 11
y = -6x - 13

• (-8, 35)

• (8, -13)

• (1, 8)

• (2, 13)

Solve the system by substitution. 
y = 2x − 11 
2x − 8y = 4 

•  (6, 1)

• (6, −4)

• (6, −1)

• Infinite number of solutions  

Solve the system by substitution. 
-2x - 2y = 16
y = -8

• (0, -8)

• (-8, 0)

• (-16, -8)

• (-16, -8)

Solve the system by substitution. 
3x − 2y = 7 
y = 2x − 7 

• No solution 

•  (7, 7)  

•  (−7, −7)  

•  (−7, −3)