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Jamie owns a pizza shop in town and is working on paying off equipment expenses. The remaining balance of [tex]\[tex]$6,550[/tex] is financed and requires a monthly payment of [tex]\$[/tex]275[/tex]. The shop is doing well, so Jamie can afford to pay an extra [tex]\$300[/tex] each month to speed up paying off the balance.

Write the second equation in a system that Jamie can use to find how many months it will take her to pay off the balance.

Equation 1: [tex]y = 300x[/tex]

Equation 2: [tex]y =[/tex]



Answer :

To solve the problem, we need to write the second equation in the system to find out how many months [tex]\( x \)[/tex] it will take Jamie to pay off the balance.

### Understanding the Problem:
1. Remaining balance: [tex]\( \$6,550 \)[/tex]
2. Regular monthly payment: [tex]\( \$275 \)[/tex]
3. Extra payment per month: [tex]\( \$300 \)[/tex]

Jamie makes a total monthly payment that is the sum of the regular monthly payment and the extra payment:
[tex]\[ \text{Total monthly payment} = \$275 + \$300 = \$575 \][/tex]

### Variables Definition:
- Let [tex]\( x \)[/tex] represent the number of months.
- Let [tex]\( y \)[/tex] represent the remaining balance after [tex]\( x \)[/tex] months.

### First Equation:
Given in the problem:
[tex]\[ y = 300x \][/tex]

### Second Equation:
To find the relationship between [tex]\( y \)[/tex] and [tex]\( x \)[/tex], we need to consider how the remaining balance decreases over time:
- Initially, the remaining balance is [tex]\( \$6,550 \)[/tex].
- Each month, Jamie pays [tex]\( \$575 \)[/tex].

So, after [tex]\( x \)[/tex] months, the balance will have decreased by [tex]\( 575x \)[/tex]:
[tex]\[ y = \$6,550 - (575x) \][/tex]

This is the second equation in the system, which represents the remaining balance as a function of the number of months passed.

### Therefore, the second equation is:
[tex]\[ y = 6550 - 575x \][/tex]

So:
[tex]\[ \text{Equation 2: } y = 6550 - 575x \][/tex]