Questions: Solve the system of two linear inequalities graphically. y - 4x > 8 y > -3 Find the region with points that satisfy both inequalities.

Transcript text: Solve the system of two linear inequalities graphically. \[ \left\{\begin{array}{l} y-4 x>8 \\ y>-3 \end{array}\right. \] Step 3 of 3 : Find the region with points that satisfy both inequalities.

Solution

Solution Steps

Step 1: Graph the first inequality \( y - 4x > 8 \)

Rewrite the inequality in slope-intercept form: \[ y > 4x + 8 \] Graph the line \( y = 4x + 8 \) with a dashed line (since the inequality is strict) and shade the region above the line.

Step 2: Graph the second inequality \( y > -3 \)

Graph the line \( y = -3 \) with a dashed line (since the inequality is strict) and shade the region above the line.

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.