Solving Systems of Equations by Substitution

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 the system of equations.

• (-23, 4)

• (-4, -3)

• (-2, -4)

• No solution

• Infinite solutions

Solve the system of equations.

• (10, 3)

• (6, 3)

• (15, 3)

• No solution

• Infinite Solution

What is the solution to this system?
x= 7 - 2y
2x + y = 5

• (-1,4)

• (4,-1)

• (1,3)

• (3,1)

When solving a system of equations algebraically, which statement results in infinite solutions?

• 4 = 7

• 2 = 2

• -3 = 3

• all of the above

When solving a system of equations algebraically, which statement results in no solution?

• 4 = 7

• -2 = 2

• -3 = 3

• all of the above

Which graph represents a system of equations with infinite solutions?

• 
• 
• 
• None of the above

Solve the system of equations.

• (11, 21)

• (3, 11)

• (11, -67)

• No solution

• Infinite solutions

Solve the system of equations.

• (-6, 30)

• (-2, 10)

• (44, 39)

• No solution

• Infinite solutions