Questions: Solve the system of two linear inequalities graphically. y ≤ 2x - 3 y > -6x + 9

Solve the system of two linear inequalities graphically. y ≤ 2x - 3 y > -6x + 9
Transcript text: Solve the system of two linear inequalities graphically. \[ \left\{\begin{array}{l} y \leq 2 x-3 \\ y>-6 x+9 \end{array}\right. \]
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Solution

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Solution Steps

Step 1: Identify the first linear inequality

The first linear inequality given is \( y \leq 2x - 3 \).

Step 2: Determine the boundary line

The boundary line for the inequality \( y \leq 2x - 3 \) is \( y = 2x - 3 \). Since the inequality is \( \leq \), the boundary line will be solid.

Step 3: Find two points on the boundary line

To graph the line \( y = 2x - 3 \), we need two points:

  1. When \( x = 0 \): \[ y = 2(0) - 3 = -3 \] So, the point is \( (0, -3) \).

  2. When \( x = 2 \): \[ y = 2(2) - 3 = 4 - 3 = 1 \] So, the point is \( (2, 1) \).

Final Answer

  • Choose a solid boundary line.
  • Enter the points \( (0, -3) \) and \( (2, 1) \) on the boundary line.
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