The given system of inequalities can be represented as follows:
1. xx ≥ 0 (The number of dimes must be greater than or equal to 0)
2. yy ≥ 0 (The number of nickels must be greater than or equal to 0)
3. xx + yy ≤ 20 (The total number of coins must be no more than 20)
4. 0.10xx + 0.05yy ≥ 1.30 (The total value of coins must be no less than $1.30)
To solve this system of inequalities graphically, we will plot these inequalities on a coordinate plane.
First, let's graph the inequality xx + yy ≤ 20:
- Plot the line xx + yy = 20.
- Shade all the points below the line, including the line itself, since it is a less than or equal to inequality.
Next, let's graph the inequality 0.10xx + 0.05yy ≥ 1.30:
- Plot the line 0.10xx + 0.05yy = 1.30.
- Shade all the points above the line, since it is a greater than or equal to inequality.
The graph will consist of two shaded areas: one below the line xx + yy = 20 and another above the line 0.10xx + 0.05yy = 1.30. The feasible solution corresponds to the region where these two shaded areas overlap.
One possible solution in this overlapping region is (xx, yy) = (10, 10). This means Mayerlin has 10 dimes and 10 nickels.
Note: There could be other possible solutions in the overlapping region, but (10, 10) is one of them.
Mayerlin has xx dimes and yy nickels. She has no more than 20 coins worth no less than $1.30 combined. Solve this system of inequalities graphically and determine one possible solution.
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