Question

Consider the following system of linear inequalities:

1. y = -x + 5
2. y > 2
3. 2 > 0
Which of the following ordered pairs are solutions to this system of inequalities?

A) (2, 5)
B) (1, 4)
C) (1, 2)
D) (3, 0)

Choose the correct option and explain your choice."

Answer 1

To determine the solution to the system of inequalities, we need to plug in the values of the ordered pairs into each inequality and check if the inequality is true. The ordered pair (2, 5) satisfies all three inequalities, making it the solution to the system.

Step-by-step explanation:

In order to determine which of the ordered pairs are solutions to the given system of inequalities, we need to evaluate each ordered pair in each inequality and see if it satisfies the inequality. Let's plug in the values for x and y from each ordered pair into each inequality and check if the inequality is true.

For example, let's take ordered pair (2, 5) and plug it into each inequality:

1. y = -x + 5: substituting x = 2 and y = 5 gives us 5 = -2 + 5, which is true.
2. y > 2: substituting x = 2 and y = 5 gives us 5 > 2, which is true.
3. 2 > 0: this is a true statement.

Since all three inequalities are true for the ordered pair (2, 5), it is a solution to the system of inequalities. We can follow the same process for the other ordered pairs to determine if they are solutions or not. By checking each ordered pair in the given system of inequalities, we find that the solution is option A) (2, 5).