Questions: Solve the system of two linear inequalities graphically. y<4 y ≥ -4 Step 3 of 3 : Find the region with points that satisfy both inequalities.

Transcript text: Solve the system of two linear inequalities graphically. \[ \left\{\begin{array}{l} y<4 \\ y \geq-4 \end{array}\right. \] Step 3 of 3 : Find the region with points that satisfy both inequalities.

Solution

Solution Steps

Step 1: Graph the first inequality \( y < 4 \)

Draw a horizontal dashed line at \( y = 4 \) because the inequality is strict (less than).
Shade the region below this line to represent \( y < 4 \).

Step 2: Graph the second inequality \( y \geq -4 \)

Draw a horizontal solid line at \( y = -4 \) because the inequality is inclusive (greater than or equal to).
Shade the region above this line to represent \( y \geq -4 \).

Step 3: Identify the region that satisfies both inequalities

The solution to the system of inequalities is the region where the shaded areas from both inequalities overlap.
This region is between the lines \( y = 4 \) and \( y = -4 \).

Final Answer

The region that satisfies both inequalities is the horizontal strip between \( y = 4 \) and \( y = -4 \).
On the given graph, this corresponds to region B.

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