Question

1. (a.e1.2, 10 points)

circle 4 ordered pairs that are solutions to this
system of inequalities.
\

$$\begin{cases} y > -2x - 1 \\\\ y \\leq 5x - 4 \\end{cases}$$

answer choices
\

$$\begin{tabular}{|c|c|c|c|} \\hline (-4, 3) & (0, 4) & (1, 1) & (1, -3) \\\\ \\hline (3, -1) & (4, 3) & (6, 0) & (-4, -4) \\\\ \\hline \\end{tabular}$$

Explanation:

Step1: Test (-4, 3)

Check \( y > -2x - 1 \): \( 3 > -2(-4) - 1 = 8 - 1 = 7 \)? No. So (-4, 3) is not a solution.

Step2: Test (0, 4)

Check \( y > -2x - 1 \): \( 4 > -2(0) - 1 = -1 \)? Yes. Check \( y \leq 5x - 4 \): \( 4 \leq 5(0) - 4 = -4 \)? No. So (0, 4) is not a solution.

Step3: Test (1, 1)

Check \( y > -2x - 1 \): \( 1 > -2(1) - 1 = -3 \)? Yes. Check \( y \leq 5x - 4 \): \( 1 \leq 5(1) - 4 = 1 \)? Yes. So (1, 1) is a solution.

Step4: Test (1, -3)

Check \( y > -2x - 1 \): \( -3 > -2(1) - 1 = -3 \)? No. So (1, -3) is not a solution.

Step5: Test (3, -1)

Check \( y > -2x - 1 \): \( -1 > -2(3) - 1 = -7 \)? Yes. Check \( y \leq 5x - 4 \): \( -1 \leq 5(3) - 4 = 11 \)? Yes. So (3, -1) is a solution.

Step6: Test (4, 3)

Check \( y > -2x - 1 \): \( 3 > -2(4) - 1 = -9 \)? Yes. Check \( y \leq 5x - 4 \): \( 3 \leq 5(4) - 4 = 16 \)? Yes. So (4, 3) is a solution.

Step7: Test (6, 0)

Check \( y > -2x - 1 \): \( 0 > -2(6) - 1 = -13 \)? Yes. Check \( y \leq 5x - 4 \): \( 0 \leq 5(6) - 4 = 26 \)? Yes. So (6, 0) is a solution.

Step8: Test (-4, -4)

Check \( y > -2x - 1 \): \( -4 > -2(-4) - 1 = 7 \)? No. So (-4, -4) is not a solution.

Answer:

(1, 1), (3, -1), (4, 3), (6, 0)