Systems of Equations: Mixed Review

A group of children and adults went to the movies. They bought 2 adult tickets and 4 children tickets for $43.00. Another group bought 2 adult and two children tickets for $30.00. How much does it cost for one child ticket?

• $8.50
• $6.50
• $5.50
• $7.50

What is the value of x+y?
x - y = 6
y= 2x - 5

• 4
• 2
• -8
• -6

Solve the following system by graphing.  What is the solution?

• Infinite number of solutions
• (3, 3)
• (3, -3)
• (-3, 3)

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. She can give 2 haircuts and 4 hair dyes takes 450 minutes.  Which system of equations represents the situation?

• 3x + 2y = 315
  2x + 4y = 450
• 3x + 2y = 450
  2x + 4y = 315
• 2x + 2y = 315
  3x + 4y = 450
• 4x+2y = 315
  3x + 2y = 450

Katie and Joan are buying coffee and tea for a party. Two pounds of coffee and 3 pounds of tea costs $19.00. Five pounds of coffee and 6 pounds of tea costs $41.50. 
How much per pound is the price of coffee?

• $3.50
• $4.00
• $7.50
• $24.50

^{What is the solution?} 

• 1
• -2
• (1, 2)
• (1, -1)

Solve:
x = -3y - 17
2x + 3y = -7

• (1, -20)
• (3, 0)
• (-5, -2)
• (10 , -9)

Solve by elimination 
-2x + 6y = 16
-4x  - 3y = 2

• (2,2)
• (-2, -2) 
• (-2,2)
• (2,1)

What is the solution to the system?
x - 2y = 2
3x + 4y = 3

• (1.4, -0.3)
• (3.1, 5)
• (-2.5, 3.5)
• (6.9, 1.02)

Solve using elimination.
8x+y=-16
-3x+y=-5

• (-1,-8)
• (-8,-1)
• (-1,8)
• (8,-1)