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1 year ago

Which ordered pairs are in the solution set of the system of linear inequalities?

Mathematics

1 answer:

Anna [14]1 year ago

3 0

The ordered pairs (5 , -2) , (3 , 1) , (4 , 2) are in the set of the solution (Option C)

<h3>What is an ordered pair?</h3>

An ordered pair is a composite of the x coordinate (abscissa) and the y coordinate (ordinate), with two values expressed between parenthesis in a predetermined order.

It aids visual comprehension by locating a point on the Cartesian plane.

<h3>How do we arrive at the solution?</h3>

The first line has negative slope and passing through points (0 , 0) and (4 , -2)

That is y > (-1/2)x

The second line has positive slope and passing through points (-2 , 0) and (2 , 2)

That is: y < (1/2)x + 1.

- Refer to the accompanying diagram to discover the common component of the solutions.

- The inequity is shown by the red shading.

- The inequity is shown by the blue shading.

- The two-colored shaded area reflects the common solutions to the two inequalities.

- Let's discover the ordered pairs in the system of linear inequalities' solution set.

- Points (-4, 2), (-3, 1), (4, -3) define the common shaded area.

- Points (5, -2), (3, 1), (3, -1) (4 , 2)

As a result, Point (5, -2) is in the darkened region.

As a result, Point (3, 1) is in the darkened area.

As a result, Point (4, 2) is in the darkened area.

As a result, the ordered pairings (5, -2), (3, 1), (4, 2) are in the solution set.

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MA_775_DIABLO [31]

The solution depends on the value of $k$ . To make things simple, assume $k>0$ . The homogeneous part of the equation is

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For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be $y_p=ae^{4x}+be^x$ . Then

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