System of Multiple Linear Equations

On the first night, the Movie House Theater sold 7 adult tickets and 11 child tickets for $227. On the second night they took in $150 by selling 6 adult tickets and 6 child tickets. Find the price of an adult ticket and the price of a child ticket.

• Adult $13
  Child $5

• Adult $10
  Child $6

• Adult $8
  Child $16

• Adult $12
  Child $13

How many solutions will this system have?

• No Solution

• Infinitely Many Solutions

• No Clue

• One solution

^{What is the solution?} 

• 1

• -2

• (1, 2)

• (1, -1)

If a system of linear equations has infinitely many solutions, what does this mean about the two lines? 

• Intersecting lines

• Same line

• Parallel lines

Solve by graphing.
y = 2x + 1
y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

Solve:
y = -1x - 5
4x - 8y = 4

• (-3, -2)

• (5, -7)

• (3, 9)

• (-5, 4)

The system of equations is given. y = x - 3 -5x - 2y = -8 Which graph shows the solution for the system of equations?

• Graph A

• Graph B

• Graph C

The system of equations is graphed incorrectly by a student. The student claims that (0, 2) is a solution to the system of linear equations because this ordered pair satisfies the first equation. 2x + 3y = 6 4x − 2y = 8 Which statement BEST explains the error in the graph and the claim of the student?

• The line 4x − 2y = 8 is graphed incorrectly. A solution for the system of linear equations must be true for both equations, not just one equation.

• The line 2x + 3y = 6 is graphed incorrectly. This system of equations has no solutions when graphed correctly.

• The line 4x − 2y = 8 is graphed incorrectly. This system of equations has no solutions when graphed correctly.

• The line 2x + 3y = 6 is graphed incorrectly. A solution for the system of linear equations must be true for both equations, not just one equation.

A florist charges for flower arrangements based on the number of each type of flower in the arrangement. Different types of flowers have different costs. An arrangement of 12 carnations and 12 roses cost $60. An arrangement of 16 carnations and 8 roses cost $52. The system shown can be used to determine the cost of each carnation, x, and rose, y. { 12x + 12y = 60 { 16x + 8y = 52 Which graph correctly represents the system and correctly labels the point, or points, which represents the solution for how much each type of flower costs?

• Graph A

• Graph B

Two students solved a system of equations. Original system: 5x - 11y = -34 8x - 12y = -4 Student 1: 8x = 12y - 4 x = 3/2 y - 1/2 5(3/2 y - 1/2) - 11y = -34 15/2 y - 5/2 - 11y = -34 -7/2 y = -63/2 y = 9 Student 2: -40x + 88y = -42 40x - 60y = -20 28y = -62 y = -2 3/14 Why did the students come up with different values for the variable y?

• Student 1 incorrectly transformed the first equation.

• Student 1 incorrectly divided in the last step.

• Student 2 incorrectly transformed the first equation.

• Student 2 incorrectly divided in the last step.