Questions: Which system of linear inequalities is represented by the graph? y ≥ x-2 and y ≤ x+1 y < x-2 and y > x+1 y ≤ x-2 and y ≥ x+1 y > x-2 and y < x+1

Which system of linear inequalities is represented by the graph? y ≥ x-2 and y ≤ x+1 y < x-2 and y > x+1 y ≤ x-2 and y ≥ x+1 y > x-2 and y < x+1
Transcript text: Which system of linear inequalities is represented by th graph? $y \geq x-2$ and $y \leq x+1$ $yx+1$ $y \leq x-2$ and $y \geq x+1$ $y>x-2$ and $y
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Solution

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Solution Steps

Step 1: Identify the lines on the graph

The graph shows two lines:

  1. The line with a positive slope passing through points like (0, -2) and (2, 0).
  2. The line with a positive slope passing through points like (0, 1) and (1, 2).
Step 2: Determine the equations of the lines
  1. The first line has a slope of 1 and a y-intercept of -2, so its equation is \( y = x - 2 \).
  2. The second line has a slope of 1 and a y-intercept of 1, so its equation is \( y = x + 1 \).
Step 3: Identify the shaded regions
  1. The region above the line \( y = x - 2 \) is shaded, indicating \( y \geq x - 2 \).
  2. The region below the line \( y = x + 1 \) is shaded, indicating \( y \leq x + 1 \).

Final Answer

The system of linear inequalities represented by the graph is: \[ y \geq x - 2 \text{ and } y \leq x + 1 \]

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