Questions: Which set of inequalities represents the solution to the system of inequalities shown in the graph?

Solution Steps

• The red line passes through points (0,0) and (4,8), so its slope \( m \) is \( \frac{8-0}{4-0} = 2 \). The equation is \( y = 2x \).
• The blue dashed line passes through points (0,0) and (2,4), so its slope \( m \) is \( \frac{4-0}{2-0} = 2 \). The equation is \( y = 2x \).

• For the red line \( y = 2x \), the shaded region is above the line, so the inequality is \( y \geq 2x \).
• For the blue dashed line \( y = 2x \), the shaded region is below the line, so the inequality is \( y \leq 2x \).

• The system of inequalities is: \[ \begin{cases} y \geq 2x \\ y \leq 2x \end{cases} \]

Final Answer