To represent constraints for the given investment and savings account equations, we first need to establish the context for time and account balance.
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Time Constraint: The variable \( x \) represents the number of years, which must be non-negative. Therefore, the inequality for the constraint on the time in years is:
\[ x \geq 0 \]
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Account Balance Constraints: The account balances \( y \) for both accounts must also be non-negative, meaning:
For the investment account: \[ y = 700(1.06)^x \geq 0 \]
And for the savings account: \[ y = 1000(1.048)^x \geq 0 \]
Since \( 700(1.06)^x \) and \( 1000(1.048)^x \) are both positive for \( x \geq 0 \), we can express this general requirement as:
\[ y \geq 0 \]
Thus, compiling the constraints, we can summarize:
The inequality for the constraint on the time in years is: \[ x \geq 0 \]
And on the account balance is: \[ y \geq 0 \]
- Viable Solutions: Since both \( x \) and \( y \) must be non-negative, the viable solutions will be in Quadrant I of the Cartesian coordinate system, where both \( x \) and \( y \) values are greater than or equal to zero.
To summarize the answers:
The inequality for the constraint on the time in years is \[ x \geq 0 \] and on the account balance is \[ y \geq 0 \] The viable solutions will be in Quadrant I.