Answer:
Option A. The student incorrectly used < instead of > for the second inequality. The correct inequality is >.
Step-by-step explanation:
Defintions:
Boundary lines that are often used in systems of linear inequalities determine the location of the solutions region in a coordinate plane.
- Solid boundary lines are used for the equal sign, "=," and the inequality symbols "≥" and "≤." This implies that the points along the line (endpoints) are included as solutions to the given system.
- Dashed boundary lines are used for inequality symbols, ">" and "<." Using the dashed lines as the boundary implies that the points along the line (endpoints) are not included as solutions to the given system.
Solution:
Given the systems of linear inequalities: y ≤ 0.5x + 1 and y = -2x + 1:
In order to determine what is the appropriate inequality symbols for both equations, we must first set the second equation with an equal sign. Then, choose a test point (not in either lines) to determine which half-plane region must be shaded.
Test point: (0, 0)
Substitute the test point into both equations to determine whether it satisfies the given equation:
y ≤ 0.5x + 1
0 ≤ 0.5(0) + 1
0 ≤ 0 + 1
0 ≤ 1 (True statement).
y = -2x + 2
0 = -2(0) + 2
0 = 0 + 2
0 = 2 (False statement). Therefore, the half-plane region that doesn't contain the test point must be shaded. Hence, we must use the ">" symbol for this equation, as we're shading "above" where the values for y is greater than the y-intercept, (0, 2).
Therefore, the correct answer is Option A: The student incorrectly used < instead of > for the second inequality. The correct inequality is > (greater than symbol).
