The correct option is A
Explanation:
First of all, let's plot the following linear equations:
[tex]\begin{array}{c}(1)\\(2)\end{array}\left\{ \begin{array}{c}y=-\frac{2}{5}x-\frac{2}{5}\\y=\frac{3}{2}x-1\end{array}\right.[/tex]
So we get the lines in the First Figure below.
- Note. he orange straight line is the yellow one in the original figure.
Both lines are dashed, so both inequalities will include symbol =. To know what is the shaded region, we need to test a point in order to know which symbol we must use in each inequality (≥ or ≤). So let's choose the origin:
[tex]\bullet \ For: \ y=-\frac{2}{5}x-\frac{2}{5} \\ \\ 0 \ (?) \ -\frac{2}{5}(0)-\frac{2}{5} \\ \\ 0 \ (?) -\frac{2}{5} \\ \\ So: \ (?)\rightarrow 0\geq -\frac{2}{5} \\ \\ So \ the \ inequality \ is: \\ \\ y\geq -\frac{2}{5}x-\frac{2}{5} \\ \\ \\ \bullet \ For: \ y=\frac{3}{2}x-1 \\ \\ 0 \ (?) \ \frac{3}{2}(0)-1\\ \\ 0 \ (?) -1 \\ \\ So: \ (?)\rightarrow 0\geq -1 \\ \\ So \ the \ inequality \ is: \\ \\ y\geq \frac{3}{2}x-1[/tex]
Finally, the correct option is A
Learn more:
Solution to the system of inequalites: https://brainly.com/question/12261425
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