Let's determine the linear equations for both options where the variable [tex]\( y \)[/tex] represents the total cost and the variable [tex]\( x \)[/tex] represents the number of tickets purchased.
### Option 1:
In this option, the cost per ticket is \[tex]$53, and there's an additional shipping fee of \$[/tex]10. The relationship between the number of tickets ([tex]\( x \)[/tex]) and the total cost ([tex]\( y \)[/tex]) can be formulated as follows:
[tex]\[ y = 53x + 10 \][/tex]
#### Explanation:
- [tex]\( 53x \)[/tex]: This term represents the total cost of [tex]\( x \)[/tex] tickets at \[tex]$53 each.
- \( +10 \): This is the constant shipping fee added to the total cost.
### Option 2:
In this option, each ticket costs \$[/tex]55, and there is no additional shipping fee. Therefore, the total cost ([tex]\( y \)[/tex]) depends directly on the number of tickets ([tex]\( x \)[/tex]):
[tex]\[ y = 55x \][/tex]
#### Explanation:
- [tex]\( 55x \)[/tex]: This term represents the total cost of [tex]\( x \)[/tex] tickets at \$55 each.
- Since there is no additional shipping fee, the equation does not have a constant term.
Therefore, the system of equations that represents the costs of the tickets is:
Option 1: [tex]\( y = 53x + 10 \)[/tex] \
Option 2: [tex]\( y = 55x \)[/tex]
Please write these equations in the respective boxes.
