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

Which set of inequalities represents the solution to the system of inequalities shown in the graph?
Transcript text: Which set of inequalities represents the solution to the system of inequalities shown in the graph?
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Solution

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Solution Steps

Step 1: Identify the Equations of the Lines
  • 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 \( y = 2x \).
Step 2: Determine the Inequalities
  • 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 \( y \leq 2x \).
Step 3: Combine the Inequalities
  • The system of inequalities is: \[ \begin{cases} y \geq 2x \\ y \leq 2x \end{cases} \]

Final Answer

The set of inequalities representing the solution to the system shown in the graph is: \[ \begin{cases} y \geq 2x \\ y \leq 2x \end{cases} \]

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