Question

1. which ordered pair is in the solution set of the following system of inequalities? \\(\

$$\begin{cases} 3x + 4y > 12 \\\\ y > 2x - 1 \\end{cases}$$

\\) a. (3, -5) b. (6, 0) c. (-8, -1) d. (-2, 6) 9) which ordered pair is in the solution set of the following system of inequalities? \\(\

$$\begin{cases} y \\leq 3x + 1 \\\\ x - y > 1 \\end{cases}$$

\\) a. (-1, 4) b. (4, 5) c. (-3, -6) d. (7, -2)

Explanation:

For Question 8:

Step1: Test Option A (3, -5)

First inequality: $3(3)+4(-5)=9-20=-11$, $-11>12$ is false. Reject A.

Step2: Test Option B (6, 0)

First inequality: $3(6)+4(0)=18$, $18>12$ is true.
Second inequality: $0>2(6)-1=11$, $0>11$ is false. Reject B.

Step3: Test Option C (-8, -1)

First inequality: $3(-8)+4(-1)=-24-4=-28$, $-28>12$ is false. Reject C.

Step4: Test Option D (-2, 6)

First inequality: $3(-2)+4(6)=-6+24=18$, $18>12$ is true.
Second inequality: $6>2(-2)-1=-5$, $6>-5$ is true.

Step1: Test Option A (-1, 4)

First inequality: $4 \leq 3(-1)+1=-2$, $4 \leq -2$ is false. Reject A.

Step2: Test Option B (4, 5)

First inequality: $5 \leq 3(4)+1=13$, $5 \leq 13$ is true.
Second inequality: $4-5=-1$, $-1>1$ is false. Reject B.

Step3: Test Option C (-3, -6)

First inequality: $-6 \leq 3(-3)+1=-8$, $-6 \leq -8$ is false. Reject C.

Step4: Test Option D (7, -2)

First inequality: $-2 \leq 3(7)+1=22$, $-2 \leq 22$ is true.
Second inequality: $7-(-2)=9$, $9>1$ is true.

Answer:

D. (-2, 6)

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For Question 9: