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]
