Sketch the region that corresponds to the given inequalities. 2x  +  4y  ≥  4 2x  −  4y  ≤  4 x      ≥  0 The x y-coordinate plane is given. There are 3 lines and a region labeled "solution set" on the graph. The first line enters the window in the second quadrant, goes down and right, passes through the point (−4, 3), crosses the y-axis at y = 1 crossing the vertical line, crosses the x-axis at x = 2 crossing the second line, passes through the point (4, −1), and exits the window in the fourth quadrant. The second line enters the window in the third quadrant, goes up and right, passes through the point (−4, −3), crosses the y-axis at y = −1 crossing the vertical line, crosses the x-axis at x = 2 crossing the first line, passes through the point (4, 1), and exits the window in the first quadrant. The vertical line crosses the x-axis at the origin. The solution set is below the first line, below the second line, and to the right of the vertical line. The regions outside the solution set are shaded. The x y-coordinate plane is given. There are 3 lines and a region labeled "solution set" on the graph. The first line enters the window in the second quadrant, goes down and right, passes through the point (−4, 3), crosses the y-axis at y = 1 crossing the vertical line, crosses the x-axis at x = 2 crossing the second line, passes through the point (4, −1), and exits the window in the fourth quadrant. The second line enters the window in the third quadrant, goes up and right, passes through the point (−4, −3), crosses the y-axis at y = −1 crossing the vertical line, crosses the x-axis at x = 2 crossing the first line, passes through the point (4, 1), and exits the window in the first quadrant. The vertical line crosses the x-axis at the origin. The solution set is above the first line, below the second line, and to the right of the vertical line. The regions outside the solution set are shaded. The x y-coordinate plane is given. There are 3 lines and a region labeled "solution set" on the graph. The first line enters the window in the second quadrant, goes down and right, passes through the point (−4, 3), crosses the y-axis at y = 1 crossing the vertical line, crosses the x-axis at x = 2 crossing the second line, passes through the point (4, −1), and exits the window in the fourth quadrant. The second line enters the window in the third quadrant, goes up and right, passes through the point (−4, −3), crosses the y-axis at y = −1 crossing the vertical line, crosses the x-axis at x = 2 crossing the first line, passes through the point (4, 1), and exits the window in the first quadrant. The vertical line crosses the x-axis at the origin. The solution set is above the first line, above the second line, and to the right of the vertical line. The regions outside the solution set are shaded. The x y-coordinate plane is given. There are 3 lines and a region labeled "solution set" on the graph. The first line enters the window in the second quadrant, goes down and right, passes through the point (−4, 3), crosses the y-axis at y = 1 crossing the vertical line, crosses the x-axis at x = 2 crossing the second line, passes through the point (4, −1), and exits the window in the fourth quadrant. The second line enters the window in the third quadrant, goes up and right, passes through the point (−4, −3), crosses the y-axis at y = −1 crossing the vertical line, crosses the x-axis at x = 2 crossing the first line, passes through the point (4, 1), and exits the window in the first quadrant. The vertical line crosses the x-axis at the origin. The solution set is below the first line, above the second line, and to the right of the vertical line. The regions outside the solution set are shaded. Say whether the region is bounded or unbounded. The region is bounded.The region is unbounded.     Find the coordinates of all corner points (if any). (If an answer does not exist, enter DNE.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Sketch the region that corresponds to the given inequalities.
2x  +  4y  ≥  4
2x  −  4y  ≤  4
x      ≥  0
The x y-coordinate plane is given. There are 3 lines and a region labeled "solution set" on the graph.
  • The first line enters the window in the second quadrant, goes down and right, passes through the point (−4, 3), crosses the y-axis at y = 1 crossing the vertical line, crosses the x-axis at x = 2 crossing the second line, passes through the point (4, −1), and exits the window in the fourth quadrant.
  • The second line enters the window in the third quadrant, goes up and right, passes through the point (−4, −3), crosses the y-axis at y = −1 crossing the vertical line, crosses the x-axis at x = 2 crossing the first line, passes through the point (4, 1), and exits the window in the first quadrant.
  • The vertical line crosses the x-axis at the origin.
  • The solution set is below the first line, below the second line, and to the right of the vertical line.
  • The regions outside the solution set are shaded.
The x y-coordinate plane is given. There are 3 lines and a region labeled "solution set" on the graph.
  • The first line enters the window in the second quadrant, goes down and right, passes through the point (−4, 3), crosses the y-axis at y = 1 crossing the vertical line, crosses the x-axis at x = 2 crossing the second line, passes through the point (4, −1), and exits the window in the fourth quadrant.
  • The second line enters the window in the third quadrant, goes up and right, passes through the point (−4, −3), crosses the y-axis at y = −1 crossing the vertical line, crosses the x-axis at x = 2 crossing the first line, passes through the point (4, 1), and exits the window in the first quadrant.
  • The vertical line crosses the x-axis at the origin.
  • The solution set is above the first line, below the second line, and to the right of the vertical line.
  • The regions outside the solution set are shaded.
The x y-coordinate plane is given. There are 3 lines and a region labeled "solution set" on the graph.
  • The first line enters the window in the second quadrant, goes down and right, passes through the point (−4, 3), crosses the y-axis at y = 1 crossing the vertical line, crosses the x-axis at x = 2 crossing the second line, passes through the point (4, −1), and exits the window in the fourth quadrant.
  • The second line enters the window in the third quadrant, goes up and right, passes through the point (−4, −3), crosses the y-axis at y = −1 crossing the vertical line, crosses the x-axis at x = 2 crossing the first line, passes through the point (4, 1), and exits the window in the first quadrant.
  • The vertical line crosses the x-axis at the origin.
  • The solution set is above the first line, above the second line, and to the right of the vertical line.
  • The regions outside the solution set are shaded.
The x y-coordinate plane is given. There are 3 lines and a region labeled "solution set" on the graph.
  • The first line enters the window in the second quadrant, goes down and right, passes through the point (−4, 3), crosses the y-axis at y = 1 crossing the vertical line, crosses the x-axis at x = 2 crossing the second line, passes through the point (4, −1), and exits the window in the fourth quadrant.
  • The second line enters the window in the third quadrant, goes up and right, passes through the point (−4, −3), crosses the y-axis at y = −1 crossing the vertical line, crosses the x-axis at x = 2 crossing the first line, passes through the point (4, 1), and exits the window in the first quadrant.
  • The vertical line crosses the x-axis at the origin.
  • The solution set is below the first line, above the second line, and to the right of the vertical line.
  • The regions outside the solution set are shaded.
Say whether the region is bounded or unbounded.
The region is bounded.The region is unbounded.    
Find the coordinates of all corner points (if any). (If an answer does not exist, enter DNE.)
smaller x-value(x, y)
 
 
 
 
larger x-value(x, y)
 
 
 
 
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