Which system of linear inequalities is represented by the graph?y≥2x + 1y≤2x - 2

Mathematics

2 answers:

o-na [289]4 years ago

7 0

See in the attached file

<h2>Explanation:</h2>

In this case we have the following system of inequalities:

$(1) \ y\geq 2x + 1 \\ \\ (2) \ y\leq 2x - 2$

First of all, let's plot the equations:

$y=2x + 1 \\ \\ \\ \bullet \ If \ x=0 \ then: \\ \\ y=2(0)+1 \therefore y=1 \\ \\ Point \ 1: (0,1) \\ \\ \\ \bullet \ If \ y=0 \ then: \\ \\ 0=2x+1 \therefore x=-1/2 \\ \\ Point \ 2: (-1/2,0) \\ \\ \\ The \ line \ passes \ through \ these \ two \ points$

$y=2x-2 \\ \\ \\ \bullet \ If \ x=0 \ then: \\ \\ y=2(0)-2 \therefore y=-2 \\ \\ Point \ 1: (0,-2) \\ \\ \\ \bullet \ If \ y=0 \ then: \\ \\ 0=2x-2 \therefore x=1 \\ \\ Point \ 2: (1,0) \\ \\ \\ The \ line \ passes \ through \ these \ two \ points$

From:

$(1) \ y\geq 2x + 1$

The symbol ≥ tells us that the shaded region (the red one) lies above the line and includes all the points on the line.

From:

$(2) \ y\leq 2x - 2$

The symbol ≤ tells us that the shaded region (the green one) lies under the line and includes all the points on the line.

Therefore, the graph that stands for this problem is shown below. As you can see, there is no intersection between the two shaded regions, so there is no any solution there.

<h2>Learn more:</h2>

Linear inequality: brainly.com/question/12984296

#LearnWithBrainly