A basket holds at most 14 pounds of apples and oranges. There are at least 3
pounds of apples in the basket. This graph shows the system that represents
this scenario, where x is the weight of the apples and y is the weight of the
oranges.
Which point represents a viable solution?

Answer:

D

Step-by-step explanation:

First, there must be at least 3 pounds of apples in the basket. Apples are the first number, so B and D are our options. As it is impossible to have a negative weight of oranges, D is our answer

The point that represents a viable solution is D(4, 3).

At least two linear inequalities in the same variables make up a system of linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.

The graph shows the system of inequalities:

x + y ≤ 14

x ≥ 3

y ≥ 0

where x is the weight of the apples and y is the weight of the oranges.

We need to find the point that represents a viable solution, which means it should satisfy all three inequalities.

Let's check each option:

A(2, 9):

2 + 9 ≤ 14 (satisfied)

2 < 3 (not satisfied)

9 ≥ 0 (satisfied)

A(2, 9) does not satisfy the second inequality, so it is not a viable solution.

B(3, -2):

3 + (-2) ≤ 14 (satisfied)

3 ≥ 3 (satisfied)

-2 ≥ 0 (not satisfied)

B(3, -2) does not satisfy the third inequality, so it is not a viable solution.

C(1, 14):

1 + 14 ≤ 14 (not satisfied)

1 ≥ 3 (not satisfied)

14 ≥ 0 (satisfied)

C(1, 14) does not satisfy the first inequality, so it is not a viable solution.

D(4, 3):

4 + 3 ≤ 14 (satisfied)

4 ≥ 3 (satisfied)

3 ≥ 0 (satisfied)

D(4, 3) satisfies all three inequalities, so it represents a viable solution.

Therefore, the point that represents a viable solution is D(4, 3).

To learn more about the systems of inequalities;

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