How do you graph the system #2x-y>=2# and #x-2y>=2#?

Answer 1

Firstly, we simplify the system bringing y at the left:
#{ (y<=2-2x), (2y<=2-x) :}#

#{ (y<=2-2x), (y<=1-x/2) :}#

Now you have to draw the two line in the Cartesian plane:

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Answer 2

To graph the system of inequalities (2x - y \geq 2) and (x - 2y \geq 2), follow these steps:

  1. Graph the boundary lines for each inequality by replacing the inequality symbol with an equal sign.

    • For (2x - y = 2), rearrange the equation to (y = 2x - 2) and plot the line.
    • For (x - 2y = 2), rearrange the equation to (y = \frac{1}{2}x - 1) and plot the line.
  2. Since the inequalities are "greater than or equal to," the shaded region will be above or on the boundary lines.

  3. Shade the region above or on each boundary line.

  4. The solution region for the system of inequalities is the overlapping shaded region.

  5. If needed, test a point not on the boundary lines to determine which side of each line to shade. For example, (0,0) is a common test point.

  6. Label the solution region if necessary.

  7. Ensure your graph is accurate and clear.

That's how you graph the system of inequalities (2x - y \geq 2) and (x - 2y \geq 2).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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