Question

The following inequalities form a system. y is less than or equal to two-thirds times x plus 1 y is greater than negative one-fourth times x plus 2 Which ordered pair is included in the solution to this system? (6, −2) (6, 0.5) (6, 5) (6, 8)

Answer 1

To find the ordered pair that is included in the solution to the system of inequalities, substitute the x and y values of each ordered pair into both inequalities and check if both inequalities are true. The ordered pairs (6, 0.5) and (6, 5) are included in the solution to this system of inequalities.

Step-by-step explanation:

To find the ordered pair that is included in the solution to the system of inequalities, we need to substitute the x and y values of each ordered pair into both inequalities and check if both inequalities are true. Let's go through the options:

(6, -2): Substituting x = 6 and y = -2 into the first inequality, we get -2 <= (2/3)(6) + 1, which simplifies to -2 <= 5. This inequality is not true, so this ordered pair is not included in the solution.

(6, 0.5): Substituting x = 6 and y = 0.5 into both inequalities, we get 0.5 <= (2/3)(6) + 1 and 0.5 > -1/4(6) + 2. Both inequalities are true, so this ordered pair is included in the solution.

(6, 5): Substituting x = 6 and y = 5 into both inequalities, we get 5 <= (2/3)(6) + 1 and 5 > -1/4(6) + 2. Both inequalities are true, so this ordered pair is included in the solution.

(6, 8): Substituting x = 6 and y = 8 into the first inequality, we get 8 <= (2/3)(6) + 1, which simplifies to 8 <= 5. This inequality is not true, so this ordered pair is not included in the solution.

Therefore, the ordered pairs (6, 0.5) and (6, 5) are included in the solution to this system of inequalities.

Answer 2

• (6, −2), (6, 0.5)

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Given system of inequalities:

• y ≤ 2/3x + 1
• y > - 1/4x + 2

Plot the inequality and the given points to determine which of them fall into solution area.

See attached.

As we see only two points fall in the solution area, brown zone on the bottom: (6, −2), (6, 0.5).