Questions: 9. y > -3 y >= 5x 10. y < -1 x > 4 11. y < -2 y > 2 12. y < x-1 y >= x+1 13. y >= -5 y-1 < 3x 14. x+y > 4 y >= (3/2)x - 9

9. y > -3 y >= 5x 10. y < -1 x > 4 11. y < -2 y > 2 12. y < x-1 y >= x+1 13. y >= -5 y-1 < 3x 14. x+y > 4 y >= (3/2)x - 9
Transcript text: 9. \[ \begin{array}{l} y>-3 \\ y \geq 5 x \end{array} \] 10. \[ \begin{array}{l} y<-1 \\ x>4 \end{array} \] 11. $y<-2$ \[ y>2 \] 12. \[ \begin{array}{l} y4 \\ y \geq \frac{3}{2} x-9 \end{array} \]
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Solution

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Solution Steps

Step 1: Identify the inequalities

The given system of inequalities is: \[ \begin{array}{l} x + y > 4 \\ y \geq \frac{3}{2} x - 9 \end{array} \]

Step 2: Convert inequalities to equations for graphing

Convert the inequalities to equations for graphing purposes:

  1. \( x + y = 4 \)
  2. \( y = \frac{3}{2} x - 9 \)
Step 3: Determine the solution region

The solution region is the area where both inequalities are satisfied:

  1. \( x + y > 4 \) means the region above the line \( x + y = 4 \).
  2. \( y \geq \frac{3}{2} x - 9 \) means the region above or on the line \( y = \frac{3}{2} x - 9 \).

Final Answer

The system of inequalities is: \[ \begin{array}{l} x + y > 4 \\ y \geq \frac{3}{2} x - 9 \end{array} \]

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["y = 4 - x", "y = (3/2)x - 9"], "latex_expressions": ["$x + y > 4$", "$y \\geq \\frac{3}{2} x - 9$"]}

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