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How do you solve this system of equations: #y\leq - x + 9 and y \geq - 2x + 12#?

Answer 1

Eva Adamson

See the Explanation.

Given:

#y <= -x+9#

#y>= -2x+12#

The procedure is as follows:

Graph each inequality separately.

An image of the graph is available below:

Then choose a convenient test point to determine which side of the line needs to be shaded. After that, you can observe that the solution to the system will be the area where the shaded segment from each inequality overlap one another.

Refer to the image below to view the overlapping segments and the test points used to identify the solution visually:

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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.